Percent Change & Percent Error
A gym had 8,500 members in 2012. It now has 7,000 members. What is the percent change?
17.6% decrease
Sasha deposits $800 at 8% simple interest for 6 months. How much interest does she earn?
$32
Ralph answered 80% of 70 questions correctly. How many did he get right?
56
A jacket costs $68. Laura has a 20% off coupon and pays 8% tax. What is her total cost?
Sale price = 54.40 Total = 54.40 × 1.08 = $58.75
Write 70% as a fraction in simplest form.
70÷100=7/10
A house price dropped from $180,000 to $165,000. What is the percent change?
8.33% decrease
Tony deposits $3000 at 5% interest and earns $525. How long was the money invested?
3.5 years
Sandra answered 45% of 60 questions correctly. How many did she get right?
27
Starbucks surveyed 1230 customers. If 70% prefer iced peppermint mochas, how many customers is that?
0.70×1230=861 861
Write 0.67% as a fraction.
0.67÷100=0.0067
67/10000
Marcus estimated 230 people would attend a concert. Actual attendance was 300. What is the percent error?
23.3%
Becky deposits $6450. After 5 years, the account is worth $7998. What interest rate did she earn?
4.8%
33 students prefer the Yankees. This is 16% of the class. How many students are in the class?
≈ 206 students
A restaurant bill is $73.89 with 7.25% tax and a 15% tip. What is the total bill?
After tax: 79.23 After tip: 91.12 $91.12
Convert (54 1/6)% into a fraction in simplest form.
325/600 = 13/24
A school had 1,260 students. Enrollment decreased by 7% the first year and then increased by 12% the next year. What is the overall percent change from the original enrollment?
After 7% decrease: 1260×0.93=1171.8
After 12% increase: 1171.8×1.12=1312.416
Change = 1312.416−1260=52.416
Percent change = 52.416÷1260=0.0416
4.16% increase
Heather earns 5% commission on $700 in sales plus a $200 salary. What is her total pay?
Commission = 35 Total = 235 $235
A class increased by 12% this year to 336 students. How many students were in the class last year?
336=1.12x x=336÷1.12=300
300 students last year
A store discounts a laptop by 25%, then applies a coupon for an additional 15% off the discounted price. After that, 8.875% tax is added. If the final price is $612.15, what was the original price?
Let original price = p
After 25% off: 0.75p After 15% off: 0.75p×0.85=0.6375p After tax: 0.6375p×1.08875=612.15
Solve: p=612.15÷(0.6375×1.08875) p=612.15÷0.694 p≈882
Original price ≈ $882
A store increases prices by 22% in January, decreases them by 15% in February, and increases them again by 18% in March. Write an expression for the March price using p, the original price.
January: 1.22p February: 1.22p×0.85=1.037p March: 1.037p×1.18=1.224p
Expression: 1.224p
A company’s revenue increased by 18% from 2021 to 2022. In 2023, revenue increased again by 22% and reached $1,384,320. What was the company’s revenue in 2021?
Let 2021 revenue = r
After 18% increase: 1.18r
After 22% increase: 1.18r×1.22=1.4396r
Set equal to 1,384,320: 1.4396r=1,384,320 r=1,384,320÷1.4396=961,000
Revenue in 2021 = $961,000
A salesperson earns 4% commission on the first $10,000 of sales and 7% on all sales above that. If she earned $1,480 in commission, how much did she sell?
Commission from first $10,000 = 400 Remaining commission = 1480 − 400 = 1080 This comes from 7% sales: 1080=0.07x x=1080÷0.07=15428.57
Total sales = 10,000+15,428.57=25,428.57
Total sales ≈ $25,429
A survey shows that 42 students represent 14% of the school’s band membership. The band expects a 20% increase next year. How many members will the band have next year?
Current membership: 42=0.14x x=300
After 20% increase: 300×1.20=360
360 members next year
A refrigerator is discounted 30%. During a clearance event, the discounted price is reduced another 22%. After tax of 8.25%, the final price is $1,047. What was the refrigerator’s original price?
Let original price = p
After 30% off: 0.70p After 22% off: 0.70p×0.78=0.546p After tax: 0.546p×1.0825=1047
Solve: p=1047÷(0.546×1.0825) p=1047÷0.591 p≈1772
Original price ≈ $1,772
Option A: $300/week + 5% commission Option B: $900/week, no commission
Find the minimum yearly sales needed for Option A to earn more than Option B.
Option A yearly salary: 300×52=15600
Option B yearly salary: 900×52=46800
Let sales = x
Option A total: 15600+0.05x>46800
Solve: 0.05x>31200 x>624000
Sales must exceed $624,000