2006 AMC 12B Problem 4

Attempt Problem 4 of the 2006 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2006 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

4.

Mary is about to pay for five items at the grocery store. The prices of the items are $7.99,\$7.99, $4.99,\$4.99, $2.99,\$2.99, $1.99,\$1.99, and $0.99.\$0.99. Mary will pay with a twenty-dollar bill. Which of the following is closest to the percentage of the $20.00\$20.00 that she will receive in change?
55
1010
1515
2020
2525
Answer: A
Concepts:estimationpercentage
Small hint:
Round each price to the nearest dollar to estimate the total quickly
Big hint:
The change is $20\$20 minus the total; compare it to $20\$20 as a fraction
Solution:
The prices total $18.95,\$18.95, so the change is $1.05.\$1.05. As a percentage of $20.00,\$20.00, this is 1.0520⋅100%=5.25%. \frac{1.05}{20}\cdot100\% = 5.25\%. The closest listed percentage is 5%.5\%.
Thus, the correct answer is A.
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