2007 AMC 8 Problem 1

Attempt Problem 1 of the 2007 AMC 8 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 2007 AMC 8 solutions, or check the answer key.

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

1.

Theresa’s parents have agreed to buy her tickets to see her favorite band if she spends an average of 1010 hours per week helping around the house for 66 weeks. For the first 55 weeks she helps around the house for 8,8, 11,11, 7,7, 1212 and 1010 hours. How many hours must she work for the final week to earn the tickets?
99
1010
1111
1212
1313
Answer: D
Concepts:mean
Small hint:
Find the total number of hours needed over all six weeks.
Big hint:
Compare that total with the hours Theresa already worked in the first five weeks.
Solution:
During the first 55 weeks, Theresa works for a total of 8+11+7+12+10=488+11+7+12+10=48 hours.
She promised to work 10⋅6=6010\cdot 6=60 hours in all.
This means that she has to work 60−48=1260-48=12 hours during the final week to earn the tickets.
Thus, D is the correct answer.
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