Packing Sodas And Modular Arithmetic
Probability
Level
1
Jerry has 44 boxes of soda in his truck. The cans of soda in each box are packed oddly so that there are 113 cans of soda in each box. Jerry plans to pack the sodas into cases of 12 cans to sell. After making as many complete cases as possible, how many sodas will Jerry have leftover?
The answer is 4.
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1 solution
First, we note that 44 is congruent to 8 (mod 12) and 113 is congruent to 5 (mod 12). Thus, 44 times 113 is congruent to 8 times 5, which is congruent to 40. 40 is 4 (mod 12). So, Jerry has 4 sodas left over.