Percent Applications Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Percent Applications.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Using percentages to solve real-world problems involving tax, tip, discount, markup, and simple interest.

A 20% tip on a $45 meal: 0.20×45=$90.20 \times 45 = \$9 tip, so total is $54. A 30% discount on $80: save $24, pay $56.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Percent applications use percent-of and percent-change to solve real money problems.

Common stuck point: The procedure for percent applications is the easy part; the trap is stopping at the percent amount instead of the final total. Asking "Does the problem add, remove, or grow a percent of a real amount (price, bill, loan)?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Does the problem add, remove, or grow a percent of a real amount (price, bill, loan)?

Worked Examples

Example 1

easy
A restaurant bill is $56\$56. The customer wants to leave a 15%15\% tip. What is the tip amount and the total paid?

Answer

Tip=$8.40,Total=$64.40\text{Tip} = \$8.40,\quad \text{Total} = \$64.40

First step

1
Tip: 15%×56=0.15×56=8.4015\% \times 56 = 0.15 \times 56 = 8.40.

Full solution

  1. 2
    Total: 56+8.40=$64.4056 + 8.40 = \$64.40.
  2. 3
    Alternatively, multiply by 1.151.15: 1.15×56=$64.401.15 \times 56 = \$64.40.
A tip is a percentage added to the original bill. You can compute the tip and add it, or multiply the bill by (1 + tip rate) to get the total in one step.

Example 2

medium
Emma borrows $2000\$2000 at a simple interest rate of 4.5%4.5\% per year for 33 years. How much total interest does she pay, and what is the total amount repaid?

Example 3

medium
A laptop costs $900\$900. The store applies a 15%15\% discount and then 8%8\% sales tax on the discounted price. What is the final price?

Example 4

medium
A meal subtotal is $48\$48. A 7%7\% sales tax is added, then an 18%18\% tip is calculated on the pre-tax subtotal. What is the total bill?

Example 5

hard
Maria invests $1200\$1200 at 5%5\% simple interest. How many years until interest reaches $300\$300?

Example 6

hard
$800\$800 is invested at 5%5\% simple interest. After how many years does the balance reach $1000\$1000?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A pair of shoes costs $72\$72 before 8%8\% sales tax. What is the final price?

Example 2

hard
A clothing store marks up items by 60%60\% of the wholesale cost and then offers a 25%25\% discount on the retail price. If the wholesale cost is $50\$50, what is the final selling price, and is it above or below the wholesale cost?

Example 3

easy
A $50\$50 item has a 10%10\% discount. How much do you save?

Example 4

easy
A $20\$20 meal gets a 15%15\% tip. How much is the tip?

Example 5

easy
Find 8%8\% tax on a $25\$25 purchase.

Example 6

easy
A $40\$40 shirt is marked up 25%25\%. What is the markup amount?

Example 7

easy
A $30\$30 item is 50%50\% off. What is the sale price?

Example 8

easy
$100\$100 earns 5%5\% simple interest for 1 year. How much interest?

Example 9

easy
A $60\$60 jacket is 20%20\% off. How much do you save?

Example 10

easy
A $45\$45 meal with a 20%20\% tip: what is the tip?

Example 11

medium
A $80\$80 item is 30%30\% off. What is the sale price?

Example 12

medium
A $45\$45 meal gets a 20%20\% tip. What is the total?

Example 13

medium
A $200\$200 item is 30%30\% off, then 8%8\% tax is applied to the sale price. Final cost?

Example 14

medium
$500\$500 at 4%4\% simple interest for 3 years earns how much interest?

Example 15

medium
A price rises from $40\$40 to $50\$50. What is the percent increase?

Example 16

medium
A $120\$120 coat is discounted to $90\$90. What percent off is that?

Example 17

medium
A $25\$25 book has 20%20\% added for tax. What is the total cost?

Example 18

medium
A $150\$150 item is 40%40\% off. What is the sale price?

Example 19

medium
$800\$800 at 6%6\% simple interest for 2 years earns how much interest?

Example 20

challenge
A store offers '25%25\% off, then an extra 10%10\% off the reduced price.' What single percent discount is this on a $200\$200 item?

Example 21

challenge
After a 20%20\% raise, an employee earns $36000\$36000. What was the original salary?

Example 22

challenge
$1000\$1000 is invested at 5%5\% simple interest. After how many years does the total reach $1250\$1250?

Example 23

easy
A jacket costs $80\$80 and is on sale for 25%25\% off. What is the sale price?

Example 24

easy
A $48\$48 dinner gets a 20%20\% tip. What is the total paid?

Example 25

medium
After a 20%20\% discount, a coat costs $72\$72. What was the original price?

Example 26

medium
After 6%6\% sales tax, a bike costs $265\$265. What was the pre-tax price?

Example 27

medium
A $60\$60 video game is marked up 35%35\% to set its store price. What is the store price?

Example 28

medium
Jack borrows $1500\$1500 at 6%6\% simple interest for 44 years. What is the total amount repaid?

Example 29

medium
A stock falls 20%20\% from $80\$80 to $64\$64. What percent rise from $64\$64 would return it to $80\$80?

Example 30

hard
An item costs $50\$50 wholesale, is marked up 40%40\%, then has 20%20\% taken off the marked price. Is the final price above or below cost, and by how much?

Example 31

hard
A loan of $2400\$2400 accrues $540\$540 of simple interest over 33 years. What is the annual interest rate?

Example 32

hard
A store offers "30%30\% off, plus an extra 10%10\% off the discounted price." What single percent discount is equivalent?

Example 33

medium
A printer is on sale for $170\$170 after a 15%15\% discount. What was the original price?

Example 34

medium
Two friends split a $84\$84 bill evenly and want to leave a combined 18%18\% tip. How much does each pay in total?

Example 35

medium
A retailer wants a 25%25\% markup over a $48\$48 cost. What is the selling price?

Example 36

hard
A car priced at $22,000\$22{,}000 is sold for $19,800\$19{,}800 after a discount. What is the discount percent?

Example 37

hard
A laptop costs $650\$650 after a 7%7\% sales tax. Round the pre-tax price to the nearest cent.

Example 38

challenge
A store first marks merchandise up 50%50\%, then has a 30%30\% off sale, then adds 10%10\% tax. If the cost is $40\$40, what is the final price?

Example 39

easy
Find 6%6\% simple interest on $250\$250 for 22 years.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

percent of a numberpercent change