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Solve Sales Tax, Commission, and Discount Applications

Solve sales tax applications

Solve Sales Tax Applications

Sales tax and commissions are applications of percent in our everyday lives. To solve these applications, we will follow the same strategy we used in the section on decimal operations. We show it again here for easy reference.

Remember that whatever the application, once we write the sentence with the given information (Step 2), we can translate it to a percent equation and then solve it.

Do you pay a tax when you shop in your city or state? In many parts of the United States, sales tax is added to the purchase price of an item. See . The sales tax is determined by computing a percent of the purchase price.

To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price. The result is the total cost—this is what the customer pays.

Example

Try it.

Evelyn bought a new smartphone for $\text{\$499}$ plus tax. She was surprised when she got the receipt and saw that the tax was $\text{\$42.42}.$ What was the sales tax rate for this purchase?

Solution

Identify what you are asked to find.	What is the sales tax rate?
Choose a variable to represent it.	Let $r=$ sales tax.
Write a sentence that gives the information to find it.	What percent of the price is the sales tax?
Translate into an equation.
Divide.
Simplify.
Check. Is this answer reasonable?
Yes, because 8.5% is close to 10%. 10% of $500 is $50, which is close to $42.42.
Write a complete sentence that answers the question.	The sales tax rate is 8.5%.

Condensed — the full section is in OpenStax Prealgebra 2e.

Solve Commission Applications

Sales people often receive a commission, or percent of total sales, for their sales. Their income may be just the commission they earn, or it may be their commission added to their hourly wages or salary. The commission they earn is calculated as a certain percent of the price of each item they sell. That percent is called the rate of commission.

To find the commission on a sale, multiply the rate of commission by the total sales. Just as we did for computing sales tax, remember to first convert the rate of commission from a percent to a decimal.

Example

Try it.

Helene is a realtor. She receives $\text{3\%}$ commission when she sells a house. How much commission will she receive for selling a house that costs $\text{\$260,000}?$

Solution

Identify what you are asked to find.	What is the commission?
Choose a variable to represent it.	Let $c=$ the commission.
Write a sentence that gives the information to find it.	The commission is 3% of the price.
Translate into an equation.
Simplify.
Check. Is this answer reasonable?
Yes. 1% of $260,000 is $2,600, and $7,800 is three times $2,600.
Write a complete sentence that answers the question.	Helene will receive a commission of $7,800.

Example

Try it.

Rikki earned $\text{\$87}$ commission when she sold a $\text{\$1,450}$ stove. What rate of commission did she get?

Solution

Identify what you are asked to find.	What is the rate of commission?
Choose a variable to represent it.	Let $r=$ the rate of commission.
Write a sentence that gives the information to find it.	The commission is what percent of the sale?
Translate into an equation.
Divide.
Simplify.
Change to percent form.
Check if this answer is reasonable.
Yes. A 10% commission would have been $145. The 6% commission, $87, is a little more than half of that.
Write a complete sentence that answers the question.	The commission was 6% of the price of the stove.

Condensed — the full section is in OpenStax Prealgebra 2e.

Solve Discount Applications

Applications of discount are very common in retail settings . When you buy an item on sale, the original price of the item has been reduced by some dollar amount. The discount rate, usually given as a percent, is used to determine the amount of the discount. To determine the amount of discount, we multiply the discount rate by the original price. We summarize the discount model in the box below.

The sale price should always be less than the original price. In some cases, the amount of discount is a fixed dollar amount. Then we just find the sale price by subtracting the amount of discount from the original price.

Example

Try it.

Jason bought a pair of sunglasses that were on sale for $\text{\$10}$ off. The original price of the sunglasses was $\text{\$39}.$ What was the sale price of the sunglasses?

Solution

Identify what you are asked to find.	What is the sale price?
Choose a variable to represent it.	Let $s=$ the sale price.
Write a sentence that gives the information to find it.	The sale price is the original price minus the discount.
Translate into an equation.
Simplify.
Check if this answer is reasonable.
Yes. The sale price, $29, is less than the original price, $39.
Write a complete sentence that answers the question.	The sale price of the sunglasses was $29.

In , the amount of discount was a set amount, $\text{\$10}.$ In the discount is given as a percent of the original price.

There may be times when you buy something on sale and want to know the discount rate. The next example will show this case.

Condensed — the full section is in OpenStax Prealgebra 2e.

Solve Mark-up Applications

Applications of mark-up are very common in retail settings. The price a retailer pays for an item is called the wholesale price. The retailer then adds a mark-up to the wholesale price to get the list price, the price he sells the item for. The mark-up is usually calculated as a percent of the wholesale price. The percent is called the mark-up rate. To determine the amount of mark-up, multiply the mark-up rate by the wholesale price. We summarize the mark-up model in the box below.

The list price should always be more than the wholesale price.

Example

Try it.

Adam's art gallery bought a photograph at the wholesale price of $\text{\$250}.$ Adam marked the price up $\text{40\%}.$ Find the ⓐ amount of mark-up and ⓑ the list price of the photograph.

Solution

ⓐ
Identify what you are asked to find.	What is the amount of mark-up?
Choose a variable to represent it.	Let $m=$ the amount of each mark-up.
Write a sentence that gives the information to find it.	The mark-up is 40% of the wholesale price.
Translate into an equation.
Simplify.
Check if this answer is reasonable.
Yes. The markup rate is less than 50% and $100 is less than half of $250.
Write a complete sentence that answers the question.	The mark-up on the photograph was $100.

ⓑ
Identify what you are asked to find.	What is the list price?
Choose a variable to represent it.	Let $p=$ the list price.
Write a sentence that gives the information to find it.	The list price is the wholesale price plus the mark-up.
Translate into an equation.
Simplify.
Check if this answer is reasonable.
Yes. The list price, $350, is more than the wholesale price, $250.
Write a complete sentence that answers the question.	The list price of the photograph was $350.

Key Concepts

Sales Tax The sales tax is a percent of the purchase price.
- $\text{sales tax}=\text{tax rate}⋅\text{purchase price}$
- $\text{total cost}=\text{purchase price}+\text{sales tax}$
Commission A commission is a percentage of total sales as determined by the rate of commission.
- $\text{commission}=\text{rate of commission}⋅\text{original price}$
Discount An amount of discount is a percent off the original price, determined by the discount rate.
- $\text{amount of discount}=\text{discount rate}⋅\text{original price}$
- $\text{sale price}=\text{original price }-\text{discount}$
Mark-up The mark-up is the amount added to the wholesale price, determined by the mark-up rate.
- $\text{amount of mark-up}=\text{mark-up rate wholesale price}$
- $\text{list price}=\text{wholesale price}+\text{mark up}$

Solve Sales Tax, Commission, and Discount Applications

Solve Sales Tax Applications

In the following exercises, find ⓐ the sales tax and ⓑ the total cost.

Try it.

The cost of a pair of boots was $\text{\$84}.$ The sales tax rate is $\text{5\%}$ of the purchase price.

Solution

ⓐ $4.20
ⓑ $88.20

Try it.

The cost of a refrigerator was $\text{\$1,242}.$ The sales tax rate is $\text{8\%}$ of the purchase price.

Try it.

The cost of a microwave oven was $\text{\$129}.$ The sales tax rate is $\text{7.5\%}$ of the purchase price.

Solution

ⓐ $9.68
ⓑ $138.68

Try it.

The cost of a tablet computer is $\text{\$350}.$ The sales tax rate is $\text{8.5\%}$ of the purchase price.

Try it.

The cost of a file cabinet is $\text{\$250}.$ The sales tax rate is $\text{6.85\%}$ of the purchase price.

Solution

ⓐ $17.13
ⓑ $267.13

Try it.

The cost of a luggage set $\text{\$400}.$ The sales tax rate is $\text{5.75\%}$ of the purchase price.

Try it.

The cost of a $\text{6-drawer}$ dresser $\text{\$1,199}.$ The sales tax rate is $\text{5.125\%}$ of the purchase price.

Solution

ⓐ $61.45
ⓑ $1,260.45

Try it.

The cost of a sofa is $\text{\$1,350}.$ The sales tax rate is $\text{4.225\%}$ of the purchase price.

In the following exercises, find the sales tax rate.

Try it.

Shawna bought a mixer for $\text{\$300}.$ The sales tax on the purchase was $\text{\$19.50}.$

Solution

6.5%

Try it.

Orphia bought a coffee table for $\text{\$400}.$ The sales tax on the purchase was $\text{\$38}.$

Try it.

Bopha bought a bedroom set for $\text{\$3,600}.$ The sales tax on the purchase was $\text{\$246.60}.$

Solution

6.85%

Try it.

Ruth bought a washer and dryer set for $\text{\$2,100}.$ The sales tax on the purchase was $\text{\$152.25}.$

Solve Commission Applications

In the following exercises, find the commission.

Try it.

Christopher sold his dinette set for $\text{\$225}$ through an online site, which charged him $\text{9\%}$ of the selling price as commission. How much was the commission?

Solution

$20.25

Try it.

Michele rented a booth at a craft fair, which charged her $\text{8\%}$ commission on her sales. One day her total sales were $\text{\$193}.$ How much was the commission?

Try it.

Farrah works in a jewelry store and receives $\text{12\%}$ commission when she makes a sale. How much commission will she receive for selling a $\text{\$8,125}$ ring?

Solution

$975

Try it.

Jamal works at a car dealership and receives $\text{9\%}$ commission when he sells a car. How much commission will he receive for selling a $\text{\$32,575}$ car?

Try it.

Hector receives $\text{17.5\%}$ commission when he sells an insurance policy. How much commission will he receive for selling a policy for $\text{\$4,910}?$

Solution

$859.25

Try it.

Denise receives $\text{10.5\%}$ commission when she books a tour at the travel agency. How much commission will she receive for booking a tour with total cost $\text{\$7,420}?$

In the following exercises, find the rate of commission.

Try it.

Dontay is a realtor and earned $\text{\$11,250}$ commission on the sale of a $\text{\$375,000}$ house. What is his rate of commission?

Solution

Try it.

Nevaeh is a cruise specialist and earned $\text{\$364}$ commission after booking a cruise that cost $\text{\$5,200}.$ What is her rate of commission?

Try it.

As a waitress, Emily earned $\text{\$420}$ in tips on sales of $\text{\$2,625}$ last Saturday night. What was her rate of commission?

Solution

16%

Try it.

Alejandra earned $\text{\$1,393.74}$ commission on weekly sales of $\text{\$15,486}$ as a salesperson at the computer store. What is her rate of commission?

Try it.

Maureen earned $\text{\$7,052.50}$ commission when she sold a $\text{\$45,500}$ car. What was the rate of commission?

Solution

15.5%

Try it.

Lucas earned $\text{\$4,487.50}$ commission when he brought a $\text{\$35,900}$ job to his office. What was the rate of commission?

Solve Discount Applications

In the following exercises, find the sale price.

Try it.

Perla bought a cellphone that was on sale for $\text{\$50}$ off. The original price of the cellphone was $\text{\$189}.$

Solution

$139

Try it.

Sophie saw a dress she liked on sale for $\text{\$15}$ off. The original price of the dress was $\text{\$96}.$

Solution

$81

Try it.

Rick wants to buy a tool set with original price $\text{\$165}.$ Next week the tool set will be on sale for $\text{\$40}$ off.

Solution

$125

Try it.

Angelo's store is having a sale on TV sets. One set, with an original price of $\text{\$859},$ is selling for $\text{\$125}$ off.

In the following exercises, find ⓐ the amount of discount and ⓑ the sale price.

Try it.

Janelle bought a beach chair on sale at $\text{60\%}$ off. The original price was $\text{\$44.95}$

Solution

ⓐ $26.97
ⓑ $17.98

Try it.

Errol bought a skateboard helmet on sale at $\text{40\%}$ off. The original price was $\text{\$49.95}.$

Try it.

Kathy wants to buy a camera that lists for $\text{\$389}.$ The camera is on sale with a $\text{33\%}$ discount.

Solution

ⓐ $128.37
ⓑ $260.63

Try it.

Colleen bought a suit that was discounted $\text{25\%}$ from an original price of $\text{\$245}.$

Try it.

Erys bought a treadmill on sale at $\text{35\%}$ off. The original price was $\text{\$949.95}.$

Solution

ⓐ $332.48
ⓑ $617.47

Try it.

Jay bought a guitar on sale at $\text{45\%}$ off. The original price was $\text{\$514.75}.$

In the following exercises, find ⓐ the amount of discount and ⓑ the discount rate. (Round to the nearest tenth of a percent if needed.)

Try it.

Larry and Donna bought a sofa at the sale price of $\text{\$1,344}.$ The original price of the sofa was $\text{\$1,920}.$

Solution

ⓐ $576
ⓑ 30%

Try it.

Hiroshi bought a lawnmower at the sale price of $\text{\$240}.$ The original price of the lawnmower is $\text{\$300}.$

Try it.

Patty bought a baby stroller on sale for $\text{\$301.75}.$ The original price of the stroller was $\text{\$355.}$

Solution

ⓐ $53.25
ⓑ 15%

Try it.

Bill found a book he wanted on sale for $\text{\$20.80}.$ The original price of the book was $\text{\$32}.$

Try it.

Nikki bought a patio set on sale for $\text{\$480}.$ The original price was $\text{\$850}.$

Solution

ⓐ $370
ⓑ 43.5%

Try it.

Stella bought a dinette set on sale for $\text{\$725}.$ The original price was $\text{\$1,299}.$

Solve Mark-up Applications

In the following exercises, find ⓐ the amount of the mark-up and ⓑ the list price.

Try it.

Daria bought a bracelet at wholesale cost $\text{\$16}$ to sell in her handicraft store. She marked the price up $\text{45\%}.$

Solution

ⓐ $7.20
ⓑ $23.20

Try it.

Regina bought a handmade quilt at wholesale cost $\text{\$120}$ to sell in her quilt store. She marked the price up $\text{55\%}.$

Try it.

Tom paid $\text{\$0.60}$ a pound for tomatoes to sell at his produce store. He added a $\text{33\%}$ mark-up.

Solution

ⓐ $0.20
ⓑ $0.80

Try it.

Flora paid her supplier $\text{\$0.74}$ a stem for roses to sell at her flower shop. She added an $\text{85\%}$ mark-up.

Try it.

Alan bought a used bicycle for $\text{\$115}.$ After re-conditioning it, he added $\text{225\%}$ mark-up and then advertised it for sale.

Solution

ⓐ $258.75
ⓑ $373.75

Try it.

Michael bought a classic car for $\text{\$8,500}.$ He restored it, then added $\text{150\%}$ mark-up before advertising it for sale.

Condensed — the full section is in OpenStax Prealgebra 2e.

Practice (40)

Try each one on paper first. Reveal the answer to check; verified ones can be opened in the solver for every step.

Solve $0.0875(720)$ through multiplication.
If you missed this problem, review .

Onthul het antwoord

$63$
Solve $12.96\div 0.04$ through division.
If you missed this problem, review .

Onthul het antwoord

$324$

Cathy bought a bicycle in Washington, where the sales tax rate was $\text{6.5\%}$ of the purchase price. What was

ⓐ the sales tax and
ⓑ the total cost of a bicycle if the purchase price of the bicycle was $\text{\$392}?$

Onthul het antwoord

ⓐ
Identify what you are asked to find.	What is the sales tax?
Choose a variable to represent it.	Let $t=$ sales tax.
Write a sentence that gives the information to find it.	The sales tax is 6.5% of the purchase price.
Translate into an equation. (Remember to change the percent to a decimal).
Simplify.
Check: Is this answer reasonable?
Yes, because the sales tax amount is less than 10% of the purchase price.
Write a complete sentence that answers the question.	The sales tax is $25.48.

ⓑ
Identify what you are asked to find.	What is the total cost of the bicycle?
Choose a variable to represent it.	Let $c=$ total cost of bicycle.
Write a sentence that gives the information to find it.	The total cost is the purchase price plus the sales tax.
Translate into an equation.
Simplify.
Check: Is this answer reasonable?
Yes, because the total cost is a little more than the purchase price.
Write a complete sentence that answers the question.	The total cost of the bicycle is $417.48.

Find ⓐ the sales tax and ⓑ the total cost: Alexandra bought a television set for $\text{\$724}$ in Boston, where the sales tax rate was $\text{6.25\%}$ of the purchase price.
Onthul het antwoord
1. ⓐ $45.25
2. ⓑ $769.25
Find ⓐ the sales tax and ⓑ the total cost: Kim bought a winter coat for $\text{\$250}$ in St. Louis, where the sales tax rate was $\text{8.2\%}$ of the purchase price.
Onthul het antwoord
1. ⓐ $20.50
2. ⓑ $270.50

Evelyn bought a new smartphone for $\text{\$499}$ plus tax. She was surprised when she got the receipt and saw that the tax was $\text{\$42.42}.$ What was the sales tax rate for this purchase?

Onthul het antwoord

Identify what you are asked to find.	What is the sales tax rate?
Choose a variable to represent it.	Let $r=$ sales tax.
Write a sentence that gives the information to find it.	What percent of the price is the sales tax?
Translate into an equation.
Divide.
Simplify.
Check. Is this answer reasonable?
Yes, because 8.5% is close to 10%. 10% of $500 is $50, which is close to $42.42.
Write a complete sentence that answers the question.	The sales tax rate is 8.5%.

Diego bought a new car for $\text{\$26,525}.$ He was surprised that the dealer then added $\text{\$2,387.25}.$ What was the sales tax rate for this purchase?

Onthul het antwoord

9%
What is the sales tax rate if a $\text{\$7,594}$ purchase will have $\text{\$569.55}$ of sales tax added to it?

Onthul het antwoord

7.5%

Helene is a realtor. She receives $\text{3\%}$ commission when she sells a house. How much commission will she receive for selling a house that costs $\text{\$260,000}?$

Onthul het antwoord

Identify what you are asked to find.	What is the commission?
Choose a variable to represent it.	Let $c=$ the commission.
Write a sentence that gives the information to find it.	The commission is 3% of the price.
Translate into an equation.
Simplify.
Check. Is this answer reasonable?
Yes. 1% of $260,000 is $2,600, and $7,800 is three times $2,600.
Write a complete sentence that answers the question.	Helene will receive a commission of $7,800.

Bob is a travel agent. He receives $\text{7\%}$ commission when he books a cruise for a customer. How much commission will he receive for booking a $\text{\$3,900}$ cruise?

Onthul het antwoord

$273
Fernando receives $\text{18\%}$ commission when he makes a computer sale. How much commission will he receive for selling a computer for $\text{\$2,190}?$

Onthul het antwoord

$394.20

Rikki earned $\text{\$87}$ commission when she sold a $\text{\$1,450}$ stove. What rate of commission did she get?

Onthul het antwoord

Identify what you are asked to find.	What is the rate of commission?
Choose a variable to represent it.	Let $r=$ the rate of commission.
Write a sentence that gives the information to find it.	The commission is what percent of the sale?
Translate into an equation.
Divide.
Simplify.
Change to percent form.
Check if this answer is reasonable.
Yes. A 10% commission would have been $145. The 6% commission, $87, is a little more than half of that.
Write a complete sentence that answers the question.	The commission was 6% of the price of the stove.

Homer received $\text{\$1,140}$ commission when he sold a car for $\text{\$28,500}.$ What rate of commission did he get?

Onthul het antwoord

4%
Bernice earned $\text{\$451}$ commission when she sold an $\text{\$8,200}$ living room set. What rate of commission did she get?

Onthul het antwoord

5.5%

Jason bought a pair of sunglasses that were on sale for $\text{\$10}$ off. The original price of the sunglasses was $\text{\$39}.$ What was the sale price of the sunglasses?

Onthul het antwoord

Identify what you are asked to find.	What is the sale price?
Choose a variable to represent it.	Let $s=$ the sale price.
Write a sentence that gives the information to find it.	The sale price is the original price minus the discount.
Translate into an equation.
Simplify.
Check if this answer is reasonable.
Yes. The sale price, $29, is less than the original price, $39.
Write a complete sentence that answers the question.	The sale price of the sunglasses was $29.

Marta bought a dishwasher that was on sale for $\text{\$75}$ off. The original price of the dishwasher was $\text{\$525}.$ What was the sale price of the dishwasher?

Onthul het antwoord

$450
Orlando bought a pair of shoes that was on sale for $\text{\$30}$ off. The original price of the shoes was $\text{\$112}.$ What was the sale price of the shoes?

Onthul het antwoord

$82

Elise bought a dress that was discounted $\text{35\%}$ off of the original price of $\text{\$140}.$ What was ⓐ the amount of discount and ⓑ the sale price of the dress?

Onthul het antwoord

ⓐ Before beginning, you may find it helpful to organize the information in a list.
Original price = $140
Discount rate = 35%
Amount of discount = ?

Identify what you are asked to find.	What is the amount of discount?
Choose a variable to represent it.	Let $d=$ the amount of discount.
Write a sentence that gives the information to find it.	The discount is 35% of the original price.
Translate into an equation.
Simplify.
Check if this answer is reasonable.
Yes. A $49 discount is reasonable for a $140 dress.
Write a complete sentence that answers the question.	The amount of discount was $49.

ⓑ
Original price = $140
Amount of discount = $49
Sale price = ?

Identify what you are asked to find.	What is the sale price of the dress?
Choose a variable to represent it.	Let $s=$ the sale price.
Write a sentence that gives the information to find it.	The sale price is the original price minus the discount.
Translate into an equation.
Simplify.
Check if this answer is reasonable.
Yes. The sale price, $91, is less than the original price, $140.
Write a complete sentence that answers the question.	The sale price of the dress was $91.

Find ⓐ the amount of discount and ⓑ the sale price: Sergio bought a belt that was discounted $\text{40\%}$ from an original price of $\text{\$29}.$
Onthul het antwoord
1. ⓐ $11.60
2. ⓑ $17.40
Find ⓐ the amount of discount and ⓑ the sale price: Oscar bought a barbecue grill that was discounted $\text{65\%}$ from an original price of $\text{\$395}.$
Onthul het antwoord
1. ⓐ $256.75
2. ⓑ $138.25

Jeannette bought a swimsuit at a sale price of $\text{\$13.95}.$ The original price of the swimsuit was $\text{\$31}.$ Find the ⓐ amount of discount and ⓑ discount rate.

Onthul het antwoord

ⓐ Before beginning, you may find it helpful to organize the information in a list.
Original price = $31
Amount of discount = ?
Sale price = $13.95

Identify what you are asked to find.	What is the amount of discount?
Choose a variable to represent it.	Let $d=$ the amount of discount.
Write a sentence that gives the information to find it.	The discount is the original price minus the sale price.
Translate into an equation.
Simplify.
Check if this answer is reasonable.
Yes. The $17.05 discount is less than the original price.
Write a complete sentence that answers the question.	The amount of discount was $17.05.

ⓑ Before beginning, you may find it helpful to organize the information in a list.
Original price = $31
Amount of discount = $17.05
Discount rate = ?

Identify what you are asked to find.	What is the discount rate?
Choose a variable to represent it.	Let $r=$ the discount rate.
Write a sentence that gives the information to find it.	The discount is what percent of the original price?
Translate into an equation.
Divide.
Simplify.
Check if this answer is reasonable.
The rate of discount was a little more than 50% and the amount of discount is a little more than half of $31.
Write a complete sentence that answers the question.	The rate of discount was 55%.

Find ⓐ the amount of discount and ⓑ the discount rate: Lena bought a kitchen table at the sale price of $\text{\$375.20}.$ The original price of the table was $\text{\$560}.$
Onthul het antwoord
1. ⓐ $184.80
2. ⓑ 33%
Find ⓐ the amount of discount and ⓑ the discount rate: Nick bought a multi-room air conditioner at a sale price of $\text{\$340}.$ The original price of the air conditioner was $\text{\$400}.$
Onthul het antwoord
1. ⓐ $60
2. ⓑ 15%

Adam's art gallery bought a photograph at the wholesale price of $\text{\$250}.$ Adam marked the price up $\text{40\%}.$ Find the ⓐ amount of mark-up and ⓑ the list price of the photograph.

Onthul het antwoord

ⓐ
Identify what you are asked to find.	What is the amount of mark-up?
Choose a variable to represent it.	Let $m=$ the amount of each mark-up.
Write a sentence that gives the information to find it.	The mark-up is 40% of the wholesale price.
Translate into an equation.
Simplify.
Check if this answer is reasonable.
Yes. The markup rate is less than 50% and $100 is less than half of $250.
Write a complete sentence that answers the question.	The mark-up on the photograph was $100.

ⓑ
Identify what you are asked to find.	What is the list price?
Choose a variable to represent it.	Let $p=$ the list price.
Write a sentence that gives the information to find it.	The list price is the wholesale price plus the mark-up.
Translate into an equation.
Simplify.
Check if this answer is reasonable.
Yes. The list price, $350, is more than the wholesale price, $250.
Write a complete sentence that answers the question.	The list price of the photograph was $350.

Jim's music store bought a guitar at wholesale price $\text{\$1,200}.$ Jim marked the price up $\text{50\%}.$ Find the ⓐ amount of mark-up and ⓑ the list price.
Onthul het antwoord
1. ⓐ $600
2. ⓑ $1,800
The Auto Resale Store bought Pablo's Toyota for $\text{\$8,500}.$ They marked the price up $\text{35\%}.$ Find the ⓐ amount of mark-up and ⓑ the list price.
Onthul het antwoord
1. ⓐ $2,975
2. ⓑ $11,475
The cost of a pair of boots was $\text{\$84}.$ The sales tax rate is $\text{5\%}$ of the purchase price.
Onthul het antwoord
1. ⓐ $4.20
2. ⓑ $88.20
The cost of a refrigerator was $\text{\$1,242}.$ The sales tax rate is $\text{8\%}$ of the purchase price.
The cost of a microwave oven was $\text{\$129}.$ The sales tax rate is $\text{7.5\%}$ of the purchase price.
Onthul het antwoord
1. ⓐ $9.68
2. ⓑ $138.68
The cost of a tablet computer is $\text{\$350}.$ The sales tax rate is $\text{8.5\%}$ of the purchase price.
The cost of a file cabinet is $\text{\$250}.$ The sales tax rate is $\text{6.85\%}$ of the purchase price.
Onthul het antwoord
1. ⓐ $17.13
2. ⓑ $267.13
The cost of a luggage set $\text{\$400}.$ The sales tax rate is $\text{5.75\%}$ of the purchase price.
The cost of a $\text{6-drawer}$ dresser $\text{\$1,199}.$ The sales tax rate is $\text{5.125\%}$ of the purchase price.
Onthul het antwoord
1. ⓐ $61.45
2. ⓑ $1,260.45
The cost of a sofa is $\text{\$1,350}.$ The sales tax rate is $\text{4.225\%}$ of the purchase price.
Shawna bought a mixer for $\text{\$300}.$ The sales tax on the purchase was $\text{\$19.50}.$

Onthul het antwoord

6.5%
Orphia bought a coffee table for $\text{\$400}.$ The sales tax on the purchase was $\text{\$38}.$
Bopha bought a bedroom set for $\text{\$3,600}.$ The sales tax on the purchase was $\text{\$246.60}.$

Onthul het antwoord

6.85%
Ruth bought a washer and dryer set for $\text{\$2,100}.$ The sales tax on the purchase was $\text{\$152.25}.$
Christopher sold his dinette set for $\text{\$225}$ through an online site, which charged him $\text{9\%}$ of the selling price as commission. How much was the commission?

Onthul het antwoord

$20.25
Michele rented a booth at a craft fair, which charged her $\text{8\%}$ commission on her sales. One day her total sales were $\text{\$193}.$ How much was the commission?

Symbols used here

\pm

plus or minus
Both signs at once: x = 3 ± 2 means 5 and 1.

\neq

not equal
The two sides are different.

\leq,\ \geq

less/greater than or equal
Inequalities that allow equality; < and > exclude it.

\approx

approximately equal
Equal to the precision shown, not exactly.

\sqrt{x},\ \sqrt[n]{x}

square root, n-th root
The non-negative number whose square (n-th power) is x.

a \bmod n

remainder
What is left after dividing a by n.

per cent
Per hundred: 15% = 15/100.

a : b,\ \frac{a}{b}

ratio, fraction
a for every b; a divided by b.

How to: Solve Sales Tax, Commission, and Discount Applications

Solve sales tax applications
Solve commission applications
Solve discount applications
Solve mark-up applications
Write a sentence that gives the information to find it.
Translate the sentence into an equation.
Solve the equation using good algebra techniques.
Check the answer in the problem and make sure it makes sense.

Questions people ask

Why does the order of operations matter?

Because 2 + 3 × 4 would otherwise be two different numbers. The convention (brackets, exponents, multiplication and division, addition and subtraction) exists so every reader gets the same value from the same expression.

How do I check an arithmetic answer?

Estimate first (round every number and compute roughly), then compare. If the estimate and the exact answer disagree by more than a little, one of them is wrong. The solver shows every operation, so you can find which line went astray.

Why are fractions harder than decimals?

They are not harder, they are more exact: 1/3 is a precise number, 0.333 is an approximation. Fractions need a common denominator to add, which is the one extra step people trip on.

Probeer je eigen

Parts of this page are adapted from OpenStax Prealgebra 2e (CC BY-NC-SA 4.0). Condensed and re-explained here; errors are ours.

Meer in Arithmetic

Order of operations Fractions Percentages Powers and roots