To review these concepts, go to Applications of Percents in Word Problems Study Guide.

## Applications of Percents in Word Problems Practice Questions

**Problems**

- Pat makes 3% commission on his total weekly sales. If his weekly sales total $2,350, what is his amount of commission earned?
- What is the total cost of an item that is marked $20.00 if the sales tax is 8%?
- What is the sale price of a new computer that costs $450.00 if the amount of discount is 25% off?
- If a 15% tip was left for a server, what was the amount of the tip in dollars if the total cost of the meal was $24?
- The price of a gallon of gasoline increased from $2.50 a gallon to $2.75 a gallon. What was the percent of increase?
- John's electric bill went from $68 last month to $54.40 this month. What was the percent of decrease in his bill?
- What is the total amount of interest paid on a $150 loan with an 8% interest rate and a time of 2 years?
- Henry earns $50 interest on money he invested at a 5% interest rate for 6 months. How much money did he invest?

**Solutions**

*Read and understand the question*. This question is looking for the amount of commission earned. The percent of commission and total sales are given.*Read and understand the question*. This question is asking for the total cost of an item that is marked $20.00 if the tax that needs to be added is 8% of this price.*Read and understand the question*. This question is looking for the sale price when a discount of 25% is given.*Read and understand the question*. This question asks for the amount of tip when the percent is 15%.*Read and understand the question*. This question is looking for the percent of increase in the cost of a gallon of gasoline.*Read and understand the question*. This question asks for the percent of decrease between John's electric bills.*Read and understand the question*. This question is asking for the amount of interest on a loan after 2 years.*Read and understand the question*. This question is asking for the amount of principle on an investment of 6 months.

*Make a plan*. To find the commission, use the proportion .

*Carry out the plan*. Substitute the values, and the proportion becomes . Cross multiply to get 100*x* = 7,050. Divide each side of the equation by 100 to get

*x*= $70.50

Pat made $70.50 in commission.

*Check your answer*. To check this problem, divide the answer of $70.50 by $2,350 to be sure the commission rate comes out to be 3%: 70.50 ÷ 2,350 = 0.03 = 3%. This solution is checking.

*Make a plan*. To find the sales tax, use the proportion . Then, add this amount to $20.00 for the final answer

*Carry out the plan*. Substitute the values, and the proportion becomes . Cross multiply to get 100*x* = 160. Divide each side of the equation by 100 to get

*x*= $1.60

The tax is $1.60. Thus, the total cost is $20.00 + $1.60 = $21.60.

*Check your answer*. To check this answer, divide the amount of tax by $20.00 to be sure that the tax rate is 8%: 1.60 ÷ 20 = 0.08 = 8%. This answer is checking.

*Make a plan*. To find the sale price, first find the amount of discount. Use the proportion . Then, subtract the discount from the original cost to find the sale price.

*Carry out the plan*. Substitute into the proportion and get . Cross multiply to get 100*x* = 11,250. Divide each side of the equation by 100 to get

*x*= $112.50

The discount is $112.50. Thus, the total sale price will be $450 – $112.50 = $337.50.

*Check your answer*. To check this answer, divide the amount of discount by 450 to be sure it is 25% of the original price: 112.50 ÷ 450 = 0.25 = 25%. This solution is checking.

*Make a plan*. To find the amount of tip, use the proportion .

*Carry out the plan*. Substitute into the proportion and get . Cross multiply to get 100*x* = 360. Divide each side of the equation by 100 to get

*x*= $3.60

They should leave $3.60 as a tip for the server.

*Check your answer*. To check this answer, divide the amount of the tip by $24 to be sure it is 15% of the original price: $3.60 ÷ $24 = 0.15 = 15%. This answer is checking.

*Make a plan*. To solve this problem, use the proportion . Subtract the two given amounts to find the difference.

*Carry out the plan*. Subtract the amounts to find the difference: $2.75 – $2.50 = $0.25. Substitute into the proportion and get . Cross multiply to get 2.5*x* = 25. Divide each side of the equation by 2.5 to get

*x*= 10

The percent of increase is 10%.

*Check your answer*. Substitute the solution into the proportion to check this answer. The proportion is . The cross products are each 25, so this answer is checking.

*Make a plan*. To solve this problem, use the proportion . Subtract the two given amounts to find the difference.

*Carry out the plan*. Subtract the amounts to find the difference: $68 – $54.40 = $13.60. Substitute into the proportion and get . Cross multiply to get 68*x* = 1,360. Divide each side of the equation by 68 to get

*x*= 20

The percent of decrease is 20%.

*Check your answer*. Substitute the solution into the proportion to check this answer. The proportion is . The cross products are each 1,360, so this answer is checking.

*Make a plan*. Use the formula *I* = *p* × *r* × *t*, and substitute the given values.

*Carry out the plan*. In this problem, the principle (*p*) is $150, the interest rate (*r*) is 8%, and the time (*t*) is 2 years. Substitute each value into the formula. Don't forget to change the percent to a decimal. The formula becomes *I* = (150)(0.08)(2) = $24. The interest earned is $24.

*Check your answer*. To check this answer, divide the amount of interest by the principle and the rate to see if the result is the time of 2 years: = 2 years. This question is checking.

*Make a plan*. Use the formula *I* = *p* × *r* × *t* and substitute the given values.

*Carry out the plan*. In this problem, the principle (*p*) is unknown, the interest rate (*r*) is 5%, and the time (*t*) is 6 months, or 0.5 years. This time, the interest (I) is given as $50. Substitute each value into the formula. Don't forget to change the percent to a decimal. The formula becomes 50 = (*p*)(0.05)(0.5). Multiply on the left side of the equation: 50 = 0.025*p*. Divide each side of the equation by 0.025.

- 2,000 =

*p*

The principle is $2,000.

*Check your answer*. To check this answer, divide the amount of interest by the principle and the rate to see if the result is the time of 0.5 years: = 0.5 years. This answer is checking.

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