# 6.7: Percents (Exercises)

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## 6.1 - Understand Percent

In the following exercises, write each percent as a ratio.

- 32% admission rate for the university
- 53.3% rate of college students with student loans

In the following exercises, write as a ratio and then as a percent.

- 13 out of 100 architects are women.
- 9 out of every 100 nurses are men.

In the following exercises, convert each percent to a fraction.

- 48%
- 175%
- 64.1%
- \(8 \dfrac{1}{4}\)%

In the following exercises, convert each percent to a decimal.

- 6%
- 23%
- 128%
- 4.9%

In the following exercises, convert each percent to (a) a simplified fraction and (b) a decimal.

- In 2012, 13.5% of the United States population was age 65 or over. (Source: www.census.gov)
- In 2012, 6.5% of the United States population was under 5 years old. (Source: www.census.gov)
- When a die is tossed, the probability it will land with an even number of dots on the top side is 50%.
- A couple plans to have three children. The probability they will all be girls is 12.5%.

In the following exercises, convert each decimal to a percent.

- 0.04
- 0.15
- 2.82
- 3
- 0.003
- 1.395

In the following exercises, convert each fraction to a percent.

- 3 4
- 11 5
- 3 5 8
- 2 9
- According to the Centers for Disease Control, \(\dfrac{2}{5}\) of adults do not take a vitamin or supplement.
- According to the Centers for Disease Control, among adults who do take a vitamin or supplement, \(\dfrac{3}{4}\) take a multivitamin.

In the following exercises, translate and solve.

- What number is 46% of 350?
- 120% of 55 is what number?
- 84 is 35% of what number?
- 15 is 8% of what number?
- 200% of what number is 50?
- 7.9% of what number is $4.74?
- What percent of 120 is 81.6?
- What percent of 340 is 595?

## 6.2 - Solve General Applications of Percents

In the following exercises, solve.

- When Aurelio and his family ate dinner at a restaurant, the bill was $83.50. Aurelio wants to leave 20% of the total bill as a tip. How much should the tip be?
- One granola bar has 2 grams of fiber, which is 8% of the recommended daily amount. What is the total recommended daily amount of fiber?
- The nutrition label on a package of granola bars says that each granola bar has 190 calories, and 54 calories are from fat. What percent of the total calories is from fat?
- Elsa gets paid $4,600 per month. Her car payment is $253. What percent of her monthly pay goes to her car payment?

In the following exercises, solve.

- Jorge got a raise in his hourly pay, from $19.00 to $19.76. Find the percent increase.
- Last year Bernard bought a new car for $30,000. This year the car is worth $24,000. Find the percent decrease.

## 6.3 - Solve Sales Tax, Commission, and Discount Applications

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

- The cost of a lawn mower was $750. The sales tax rate is 6% of the purchase price.
- The cost of a water heater is $577. The sales tax rate is 8.75% of the purchase price.

In the following exercises, find the sales tax rate.

- Andy bought a piano for $4,600. The sales tax on the purchase was $333.50.
- Nahomi bought a purse for $200. The sales tax on the purchase was $16.75.

In the following exercises, find the commission.

- Ginny is a realtor. She receives 3% commission when she sells a house. How much commission will she receive for selling a house for $380,000?
- Jackson receives 16.5% commission when he sells a dinette set. How much commission will he receive for selling a dinette set for $895?

In the following exercises, find the rate of commission.

- Ruben received $675 commission when he sold a $4,500 painting at the art gallery where he works. What was the rate of commission?
- Tori received $80.75 for selling a $950 membership at her gym. What was her rate of commission?

In the following exercises, find the sale price.

- Aya bought a pair of shoes that was on sale for $30 off. The original price of the shoes was $75.
- Takwanna saw a cookware set she liked on sale for $145 off. The original price of the cookware was $312.

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

- Nga bought a microwave for her office. The microwave was discounted 30% from an original price of $84.90.
- Jarrett bought a tie that was discounted 65% from an original price of $45.

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

- Hilda bought a bedspread on sale for $37. The original price of the bedspread was $50.
- Tyler bought a phone on sale for $49.99. The original price of the phone was $79.99.

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

- Manny paid $0.80 a pound for apples. He added 60% markup before selling them at his produce stand. What price did he charge for the apples?
- It cost Noelle $17.40 for the materials she used to make a purse. She added a 325% markup before selling it at her friend’s store. What price did she ask for the purse?

## 6.4 - Solve Simple Interest Applications

In the following exercises, solve the simple interest problem.

- Find the simple interest earned after 4 years on $2,250 invested at an interest rate of 5%.
- Find the simple interest earned after 7 years on $12,000 invested at an interest rate of 8.5%.
- Find the principal invested if $660 interest was earned in 5 years at an interest rate of 3%.
- Find the interest rate if $2,898 interest was earned from a principal of $23,000 invested for 3 years.
- Kazuo deposited $10,000 in a bank account with interest rate 4.5%. How much interest was earned in 2 years?
- Brent invested $23,000 in a friend’s business. In 5 years the friend paid him the $23,000 plus $9,200 interest. What was the rate of interest?
- Fresia lent her son $5,000 for college expenses. Three years later he repaid her the $5,000 plus $375 interest. What was the rate of interest?
- In 6 years, a bond that paid 5.5% earned $594 interest. What was the principal of the bond?

## 6.5 - Solve Proportions and their Applications

In the following exercises, write each sentence as a proportion.

- 3 is to 8 as 12 is to 32.
- 95 miles to 3 gallons is the same as 475 miles to 15 gallons.
- 1 teacher to 18 students is the same as 23 teachers to 414 students.
- $7.35 for 15 ounces is the same as $2.94 for 6 ounces.

In the following exercises, determine whether each equation is a proportion.

- \(\dfrac{5}{13} = \dfrac{30}{78}\)
- \(\dfrac{16}{7} = \dfrac{48}{23}\)
- \(\dfrac{12}{18} = \dfrac{6.99}{10.99}\)
- \(\dfrac{11.6}{9.2} = \dfrac{37.12}{29.44}\)

In the following exercises, solve each proportion.

- \(\dfrac{x}{36} = \dfrac{5}{9}\)
- \(\dfrac{7}{a} = \dfrac{-6}{84}\)
- \(\dfrac{1.2}{1.8} = \dfrac{d}{6}\)
- \(\dfrac{\dfrac{1}{2}}{2} = \dfrac{m}{20}\)

In the following exercises, solve the proportion problem.

- The children’s dosage of acetaminophen is 5 milliliters (ml) for every 25 pounds of a child’s weight. How many milliliters of acetaminophen will be prescribed for a 60 pound child?
- After a workout, Dennis takes his pulse for 10 sec and counts 21 beats. How many beats per minute is this?
- An 8 ounce serving of ice cream has 272 calories. If Lavonne eats 10 ounces of ice cream, how many calories does she get?
- Alma is going to Europe and wants to exchange $1,200 into Euros. If each dollar is 0.75 Euros, how many Euros will Alma get?
- Zack wants to drive from Omaha to Denver, a distance of 494 miles. If his car gets 38 miles to the gallon, how many gallons of gas will Zack need to get to Denver?
- Teresa is planning a party for 100 people. Each gallon of punch will serve 18 people. How many gallons of punch will she need?

In the following exercises, translate to a proportion.

- What number is 62% of 395?
- 42 is 70% of what number?
- What percent of 1,000 is 15?
- What percent of 140 is 210?

In the following exercises, translate and solve using proportions.

- What number is 85% of 900?
- 6% of what number is $24?
- $3.51 is 4.5% of what number?
- What percent of 3,100 is 930?

## PRACTICE TEST

In the following exercises, convert each percent to (a) a decimal (b) a simplified fraction.

- 24%
- 5%
- 350%

In the following exercises, convert each fraction to a percent. (Round to 3 decimal places if needed.)

- \(\dfrac{7}{8}\)
- \(\dfrac{1}{3}\)
- \(\dfrac{11}{12}\)

In the following exercises, solve the percent problem.

- 65 is what percent of 260?
- What number is 27% of 3,000?
- 150% of what number is 60?
- Yuki’s monthly paycheck is $3,825. She pays $918 for rent. What percent of her paycheck goes to rent?
- The total number of vehicles on one freeway dropped from 84,000 to 74,000. Find the percent decrease (round to the nearest tenth of a percent).
- Kyle bought a bicycle in Denver where the sales tax was 7.72% of the purchase price. The purchase price of the bicycle was $600. What was the total cost?
- Mara received $31.80 commission when she sold a $795 suit. What was her rate of commission?
- Kiyoshi bought a television set on sale for $899. The original price was $1,200. Find: (a) the amount of discount (b) the discount rate (round to the nearest tenth of a percent)
- Oxana bought a dresser at a garage sale for $20. She refinished it, then added a 250% markup before advertising it for sale. What price did she ask for the dresser?
- Find the simple interest earned after 5 years on $3000 invested at an interest rate of 4.2%.
- Brenda borrowed $400 from her brother. Two years later, she repaid the $400 plus $50 interest. What was the rate of interest?
- Write as a proportion: 4 gallons to 144 miles is the same as 10 gallons to 360 miles.
- Solve for a: \(\dfrac{12}{a} = \dfrac{−15}{65}\)
- Vin read 10 pages of a book in 12 minutes. At that rate, how long will it take him to read 35 pages?

## Contributors and Attributions

Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at http://cnx.org/contents/fd53eae1-fa2...49835c3c@5.191."