Question

While exploring a cave, Carl comes across a collection of $5$ -pound rocks worth $ $14$ each, $4$ -pound rocks worth $ $11$ each, and $1$ -pound rocks worth $ $2$ each. There are at least $20$ of each size. He can carry at most $18$ pounds. What is the maximum value, in dollars, of the rocks he can carry out of the cave?

$48$

$49$

$50$

$51$

$52$

Solution:

The rocks are worth $ $2.80,$ $ $2.75,$ and $ $2$ per pound respectively, so the $1$ -pound rocks are never worthwhile. Testing how many $5$ -pound rocks to take and filling the rest with $4$ -pound rocks: three $5$ -pound rocks plus three $1$ -pound rocks give $ $42 + \$6 = \$48;$ two $5$ -pound and two $4$ -pound rocks use all $18$ pounds for $ $28 + \$22 = \$50;$ one $5$ -pound, three $4$ -pound, and one $1$ -pound rock give $ $49.$

The maximum value is $ $50.$ Thus, the correct answer is C.

2018 AMC 12A Problem 2

Solution:

Problem 2 in Other Years