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Problem 238

Combinatorics Difficulty 1.4 Multiple choice CEMC Gauss (Grade 7) · Canada · 2017

At the Gaussian Store, puzzles cost $10 each or $50 for a box of 6 puzzles. If a customer would like exactly 25 puzzles, what is the minimum possible cost?

Pick one

Official solution

If puzzles are bought individually for $10 each, then 6 puzzles will cost $\$10\times6=\$60$ .

Since the cost for a box of 6 puzzles is $50, it is less expensive to buy puzzles by the box than it is to buy them individually.

Buying 4 boxes of 6 puzzles gives the customer $4\times6=24$ puzzles and the cost is $4\times\$50=\$200$ .

Buying one additional puzzle for $10 gives the customer 25 puzzles at a minimum cost of $\$210$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.