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?

$9$

$11$

$12$

$13$

$14$

Solution:

Since $2 \cdot .5 = 1,$ we have that Tony makes a dollar per day per full year of his age.

If he is $12$ at the end of the period, then Tony can make a maximum of $12 \cdot 50 = 600$ dollars in the period. If he was $13$ at the end, then he could have made $13 \cdot 50 = 650.$ By this, we can see that Tony is $13$ the end of the period, since otherwise he would make too much or too little money.

Thus, D is the correct answer.

2010 AMC 10A Problem 8

Solution:

Problem 8 in Other Years