Question

Tony works $2$ hours a day and is paid $\$0.50$ per hour for each full year of his age. During a six month period Tony worked $50$ days and earned $\$630.$ How old was Tony at the end of the six month period?

$9$

$11$

$12$

$13$

$14$

Answer: D

Concepts:ages rate bounding to limit cases

Difficulty rating: 1370

Solution:

Tony worked $2\cdot50=100$ hours, so his average hourly pay was $\$630\div100=\$6.30.$ Because his hourly pay is $\$0.50$ times his age in full years, his average age on the days he worked was $6.30\div0.50=12.6$ years. During a six-month period his age can change by at most one, so he must have worked some days at age $12$ and some at age $13.$ Thus he was $13$ at the end of the period.

Thus, D is the correct answer.

2010 AMC 10A Problem 8

Answer: D

Difficulty rating: 1370

Solution:

Problem 8 in Other Years