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Mathematics LibreTexts

6.E: Percents (Exercises)

6.1 - Understand Percent

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

  1. 32% admission rate for the university
  2. 53.3% rate of college students with student loans

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

  1. 13 out of 100 architects are women.
  2. 9 out of every 100 nurses are men.

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

  1. 48%
  2. 175%
  3. 64.1%
  4. \(8 \frac{1}{4}\)%

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

  1. 6%
  2. 23%
  3. 128%
  4. 4.9%

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

  1. In 2012, 13.5% of the United States population was age 65 or over. (Source: www.census.gov)
  2. In 2012, 6.5% of the United States population was under 5 years old. (Source: www.census.gov)
  3. When a die is tossed, the probability it will land with an even number of dots on the top side is 50%.
  4. 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.

  1. 0.04
  2. 0.15
  3. 2.82
  4. 3
  5. 0.003
  6. 1.395

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

  1. 3 4
  2. 11 5
  3. 3 5 8
  4. 2 9
  5. According to the Centers for Disease Control, \(\frac{2}{5}\) of adults do not take a vitamin or supplement.
  6. According to the Centers for Disease Control, among adults who do take a vitamin or supplement, \(\frac{3}{4}\) take a multivitamin.

In the following exercises, translate and solve.

  1. What number is 46% of 350?
  2. 120% of 55 is what number?
  3. 84 is 35% of what number?
  4. 15 is 8% of what number?
  5. 200% of what number is 50?
  6. 7.9% of what number is $4.74?
  7. What percent of 120 is 81.6?
  8. What percent of 340 is 595?

6.2 - Solve General Applications of Percents

In the following exercises, solve.

  1. 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?
  2. 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?
  3. 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?
  4. 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.

  1. Jorge got a raise in his hourly pay, from $19.00 to $19.76. Find the percent increase.
  2. 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.

  1. The cost of a lawn mower was $750. The sales tax rate is 6% of the purchase price.
  2. 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.

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

In the following exercises, find the commission.

  1. 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?
  2. 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.

  1. Ruben received $675 commission when he sold a $4,500 painting at the art gallery where he works. What was the rate of commission?
  2. 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.

  1. Aya bought a pair of shoes that was on sale for $30 off. The original price of the shoes was $75.
  2. 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.

  1. Nga bought a microwave for her office. The microwave was discounted 30% from an original price of $84.90.
  2. 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.)

  1. Hilda bought a bedspread on sale for $37. The original price of the bedspread was $50.
  2. 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.

  1. 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?
  2. 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.

  1. Find the simple interest earned after 4 years on $2,250 invested at an interest rate of 5%.
  2. Find the simple interest earned after 7 years on $12,000 invested at an interest rate of 8.5%.
  3. Find the principal invested if $660 interest was earned in 5 years at an interest rate of 3%.
  4. Find the interest rate if $2,898 interest was earned from a principal of $23,000 invested for 3 years.
  5. Kazuo deposited $10,000 in a bank account with interest rate 4.5%. How much interest was earned in 2 years?
  6. 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?
  7. 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?
  8. 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.

  1. 3 is to 8 as 12 is to 32.
  2. 95 miles to 3 gallons is the same as 475 miles to 15 gallons.
  3. 1 teacher to 18 students is the same as 23 teachers to 414 students.
  4. $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.

  1. \(\frac{5}{13} = \frac{30}{78}\)
  2. \(\frac{16}{7} = \frac{48}{23}\)
  3. \(\frac{12}{18} = \frac{6.99}{10.99}\)
  4. \(\frac{11.6}{9.2} = \frac{37.12}{29.44}\)

In the following exercises, solve each proportion.

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

In the following exercises, solve the proportion problem.

  1. 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?
  2. After a workout, Dennis takes his pulse for 10 sec and counts 21 beats. How many beats per minute is this?
  3. An 8 ounce serving of ice cream has 272 calories. If Lavonne eats 10 ounces of ice cream, how many calories does she get?
  4. 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?
  5. 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?
  6. 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.

  1. What number is 62% of 395?
  2. 42 is 70% of what number?
  3. What percent of 1,000 is 15?
  4. What percent of 140 is 210?

In the following exercises, translate and solve using proportions.

  1. What number is 85% of 900?
  2. 6% of what number is $24?
  3. $3.51 is 4.5% of what number?
  4. What percent of 3,100 is 930?

PRACTICE TEST

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

  1. 24%
  2. 5%
  3. 350%

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

  1. \(\frac{7}{8}\) 
  2. \(\frac{1}{3}\)
  3. \(\frac{11}{12}\)

In the following exercises, solve the percent problem.

  1. 65 is what percent of 260?
  2. What number is 27% of 3,000?
  3. 150% of what number is 60?
  4. Yuki’s monthly paycheck is $3,825. She pays $918 for rent. What percent of her paycheck goes to rent?
  5. 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).
  6. 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?
  7. Mara received $31.80 commission when she sold a $795 suit. What was her rate of commission?
  8. 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)
  9. 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?
  10. Find the simple interest earned after 5 years on $3000 invested at an interest rate of 4.2%.
  11. Brenda borrowed $400 from her brother. Two years later, she repaid the $400 plus $50 interest. What was the rate of interest?
  12. Write as a proportion: 4 gallons to 144 miles is the same as 10 gallons to 360 miles.
  13. Solve for a: \(\frac{12}{a} = \frac{−15}{65}\)
  14. Vin read 10 pages of a book in 12 minutes. At that rate, how long will it take him to read 35 pages?

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