# Solutions: Percent Applications

### Percent and Proportions

 Exercise Problem Solution Answer 1 What is 20% of 90? 18 2 14 out of 56 students got an A. What percent got an A? 25% 3 There are 18 girls in a class. If this is 40% of the class list, then how many students are in the class? 45 4 In a school, 25% of 312 students bring lunch from home. How many students is that? 78 5 12 out of 30 students studied Spanish. What percent studied Spanish? 40%

### Discount and Sale Price

 Exercise Problem Solution Answer 1 In a boutique, a \$14 scarf is marked, "20% off." What is the sale price of the scarf? 0.20 x \$14.00 = \$2.80 \$14.00 - \$2.80 = \$11.20 11.20 2 In an electronics store, a \$75 iPod is labeled, "Save 15%." What is the sale price of the iPod? 0.15 x \$75.00 = \$11.25 \$75.00 - \$11.25 = \$63.75 63.75 3 What is the discount for the iPod in Exercise 2? \$11.25 11.25 4 A \$30 shirt is marked, "Get off." What is the sale price of the shirt? x \$30.00 = \$10.00 \$30.00 - \$10.00 = \$20.00 20.00 or 20 5 In a bicycle store, a \$500 bicycle is marked, "Get a 30% discount." What is the sale price of the bicycle? 0.30 x \$500.00 = \$150.00 \$500 - \$150.00 = \$350.00 350.00 or 350

### Simple Interest

 Exercise Problem Solution Answer 1 Matilda invested \$5,000 at a rate of 7.5%. How much did she have after 6 months? \$5,000.00 x 0.075 x 0.5 = \$187.50 \$5,000 + \$187.50 = \$5,187.50 5187.50 or 5187.5 2 Aaron borrowed \$200 to finance a VCR at a rate of 8.25% for 1 years. How much did he repay altogether? \$200.00 x 0.0825 x 1.5 = \$24.75 \$200 + \$24.75 = \$224.75 224.75 3 Sam deposited \$400 into a savings account that earned 4 % interest per year. How much money did he have after 2.5 years? \$400 x 0.045 x 2.5 = \$45.00 \$400.00 + \$45.00 = \$445.00 445.00 or 445 4 Gabriella borrowed \$3,600 to finance a large-screen television at a rate of 6.25% for 4.75 years. How much interest did she pay? \$3,600 x 0.0625 x 4.75 = \$1,068.75 1068.75 5 Matthew deposited \$900 into a certificate of deposit with a rate of 1.5% for 6 months. How much money did he have in the account after 6 months? \$900.00 x 0.015 x 0.5 = \$6.75 \$900.00 + \$6.75 = \$906.75 906.75

### Commission

 Exercise Problem Solution Answer 1 A computer salesman earns a 5.5% commission on each sale. If he sells 5 computers in one week for a total of \$15,500, how much commission does he earn? \$15,500.00 x 0.055 = \$852.50 852.50 2 The Chen family sold their house through a real estate agent for \$330,000. If the real estate agent gets a 4.5% commission, how much will the Chen family have to pay her? \$330,000.00 x 0.045 = \$14,850.00 14580.00 or 14850 3 A pharmaceutical sales rep receives an 3.5% commission for selling medication to physicians. If he sells \$22,500 of medication, then how much commission will he earn? \$22,500.00 x 0.035 = \$787.50 787.50 or 787.5 4 A department store pays an interior designer a 25% commission for sales. How much will the department store have to pay the interior designer if her weekly sales are  \$1,875? \$1,875.00 x 0.25 = \$468.75 468.75 5 A wholesale food rep earns a 3.25% commission on sales. If her annual sales is \$35,000, how much commission will she earn? \$35,000.00 x 0.0325 = \$1,137.50 1137.50 or 1137.5

### Sales Tax

 Exercise Problem Solution Answer 1 If the sales tax rate is 7.375% in New York State, then how much sales tax would you pay in Albany for a \$34 pair of pants? 34.00 x 0.07375 = 2.5075. Rounded to the nearest cent --> \$2.51 2.51 2 If the sales tax rate is 5.25% in New Jersey, then what is the total price including tax for a \$25.00 piece of jewelry bought in Trenton? 25.00 x 0.0525 = 1.3125. Rounded to the nearest cent -->\$1.31. \$25.00 + \$1.31 = \$26.31 1.31 3 Amy bought a dress marked \$42 and then paid the store clerk a total of \$43.47. What was the sales tax rate? (Enter your answer as a percent.) \$43.47 - \$42.00 = \$1.47 1.47 ÷ 42.00 = 0.035 0.035 = 3.5% 3.5% 4 If the sales tax rate is 8.375% in New York City, then how much sales tax would you pay for a new car in Manhattan that costs \$31,500? \$31,500 x 0.08375 = \$2,638.125. Rounded to the nearest cent --> \$2,638.13. 2638.13 5 If the sales tax rate is 7.25% in California, then how much tax should a merchant charge in San Francisco for the sale of a \$15 scarf? 15.00 x 0.0725 = 1.0875. Rounded to the nearest cent --> \$1.09. 1.09

### Percent Change

 Exercise Problem Solution Answer 1 Stock in Company XYZ decreased from \$14 a share to \$9 a share.  What is the percent decrease in stock price? Rounded to the nearest tenth of a percent we get  9.1%. 2 At Furnace Woods School, enrollment increased from 320 students in 2006  to 349 students in 2007. What is the percent increase in enrollment? Rounded to the nearest tenth of a percent we get  3.6%. 3 The tuition at a college increased from 50,000 in 2006 to to 59,000 in 2007. What is the percent increase in tuition? 18% 4 The price of oil decreased from \$54 per barrel to \$50 per barrel. What is the percent decrease in oil prices? Rounded to the nearest tenth of a percent we get  7.4% 5 In a small town, the population increased from 25,000 people in 1990 to 32,000 people in 2000. What is the percent increase in population? 28%

### Practice Exercises

 Exercise Problem Solution Answer 1 What percent of 50 is 18? 36% 2 16 is 25% of what number? 64 3 What is 35% of 210? 73.5 or 73.50 4 In a department store, a pair of pants that regularly sell for \$42 is marked, "Save 15%." What is the sale price of the pants? \$42.00 x 0.15 = \$6.30 \$42.00 - \$6.30 = \$35.70 35.70 5 Sam owes \$12,000 in students loans for college. The interest rate is 8.25% and the loan will be paid off over 6 years. How much will he pay altogether? \$12,000 x 0.0825 x 6 = \$5,940 \$12,000 + \$5,940 = \$17,940 17940 or 17940.00 6 Jill put \$800 into a savings account that earns 4% in interest. How much will she have after 9 months? \$800.00 x 0.04 x 0.75 = \$24.00 \$800.00 + \$24.00 = \$824.00 824.00 or 824 7 A salesman at Wasteland TV Company sold five color TV sets for a total of \$18,990. If his commission is 5.5% of sales, how much did he earn last week? \$18,990.00 x 0.055 = \$1,044.45 1044.45 8 If the sales tax rate is 8.375% in New York City, then how much would you pay for a pair of shoes in Manhattan that cost \$125.00? (Round your answer to the nearest cent.) \$125.00 x 0.08375 = \$10.46875 \$10.46875 to the nearest cent is \$10.47 \$125.00 + \$10.47 = \$135.47 135.47 9 Gail works in as an office clerk for \$15.00 per hour. If her pay is increased to \$18.00, then what is her percent increase in pay? 20% 10 At Blue Mountain Middle School, enrollment decreased from 590 students in 2006 to 579 students in 2007. What is the percent decrease in enrollment? (Round your answer to the nearest tenth of a percent.) 1.9%

### Challenge Exercises

 Exercise Problem Solution Answer 1 At Furnace Woods school, 297 of students take the bus. If this number is 90% of the school enrollment, then how many students are enrolled? 330 2 A basketball team won 60% of 125 games played in a season? How many games is that? 75 games 3 On a roofing job, 21 out of 416 shingles had to be rejected for minor defects. What percent is this? (Round your answer to the nearest percent.) 5% 4 In a fashion boutique, a coat that regularly sell for \$150 is marked, "Get off." What is the sale price of the coat? \$150 - \$50 = \$100 100.00 or 100 5 David arranges a 36-month car loan of \$19,000 at 12.75% annual interest. Assuming equal monthly payments on principal and interest, how much will he pay monthly? (Round your answer to the nearest cent.) \$19,000 x 0.1275 x 3 = \$7,267.50 \$7,267.50 ÷ 36 = \$201.875 \$19,000 ÷ 36 = \$527.777 \$527.777 + \$201.875 = \$729.65277 729.65 6 Gisele put \$800 into a savings account that earns 6.5% simple interest for the first 3 months and 2.25% simple interest for the next 9 months. How much will she have after 1 year? \$800.00 x 0.065 x 0.25 = \$13 interest \$800.00 x 0.0225 x 0.75 = \$13.50 \$800 + \$13.00 + \$13.50 = \$826.50 826.50 or 826.5 7 The commission rate paid to a sales rep varies according to the type of equipment sold. If her monthly statement showed \$124,600 in sales and her total commission was \$4,438, then what was her rate of commission to the nearest tenth of a percent? \$4,438 ÷ \$124,600 = 0.0356179 3.6% 8 An interior designer is able to purchase a sofa from a design center for \$1,457. Her client would have to pay \$1,880 for the same sofa. What rate of discount did the designer receive for the sofa? \$1,457.00 ÷ \$1,880.00 = 0.775 100.0% - 77.5% = 22.5% 22.5% 9 The output of an electrical circuit increases from 19 amperes to 22 amperes. What is the percent increase in the output? (Round your answer to the nearest tenth of a percent.) 15.8% 10 The reading on a pressure valve decreases from 36 psi to 30 psi. What is the percent decrease in pressure? (Round your answer to the nearest tenth of a percent.) 16.7%