2018 AMC 12A Problem 2
Problem 2 of 25EasierProblem-Solving Techniques
While exploring a cave, Carl comes across a collection of -pound rocks worth each, -pound rocks worth each, and -pound rocks worth each. There are at least of each size. He can carry at most pounds. What is the maximum value, in dollars, of the rocks he can carry out of the cave?
Answer choices
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Solution
The rocks are worth and per pound, respectively. For each possible number of -pound rocks, use as many -pound rocks as fit and fill any leftover capacity with -pound rocks. Taking or of the -pound rocks gives maximum values and respectively.
Thus two -pound and two -pound rocks use all pounds, and the maximum value is Thus, the correct answer is C.
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