Solutions: Percent Applications

If you would like to better understand the curriculum, here are the learning objectives for this unit.

Percent and Proportions

Exercise Problem Solution Answer
1 What is 20% of 90? prop_solns_ex1.gif 18
2 14 out of 56 students got an A. What percent got an A? prop_solns_ex2.gif 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? prop_solns_ex3.gif 45
4 In a school, 25% of 312 students bring lunch from home. How many students is that? prop_solns_ex4.gif 78
5 12 out of 30 students studied Spanish. What percent studied Spanish? prop_solns_ex5.gif 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 1_over_3.gif off.” What is the sale price of the shirt? 1_over_3.gif 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 1_over_2_1.gif 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 41_over_2_1.gif% 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? percent_change_solns_ex1.gif 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? percent_change_solns_ex2.gif 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? percent_change_solns_ex3.gif 18%
4 The price of oil decreased from $54 per barrel to $50 per barrel. What is the percent decrease in oil prices? percent_change_solns_ex4.gif 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? percent_change_solns_ex5.gif 28%

Practice Exercises

Exercise Problem Solution Answer
1 What percent of 50 is 18? practice_solns_ex1.gif 36%
2 16 is 25% of what number? practice_solns_ex2.gif 64
3 What is 35% of 210? practice_solns_ex3.gif 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? practice_solns_ex9.gif 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.) practice_solns_ex10.gif 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? challenge_solns_ex1.gif 330
2 A basketball team won 60% of 125 games played in a season? How many games is that? challenge_solns_ex2.gif 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.) challenge_solns_ex3.gif 5%
4 In a fashion boutique, a coat that regularly sell for $150 is marked, “Get 1_over_3.gif off.” What is the sale price of the coat? challenge_solns_ex4.gif$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.) challenge_solns_ex9.gif 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.) challenge_solns_ex10.gif 16.7%