CEMC Fermat

Algebra Difficulty 2.7 Junior Find the answer

When $k$ candies were distributed among seven people so that each person received the same number of candies and each person received as many candies as possible, there were 3 candies left over. If instead, $3 k$ candies were distributed among seven people in this way, then how many candies would have been left over?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Suppose that each of the 7 people received $q$ candies under the first distribution scheme. Then the people received a total of $7 q$ candies and 3 candies were left over. Since there were $k$ candies, then $k=7 q+3$ . Multiplying both sides by 3, we obtain $3 k=21 q+9$ . When $21 q+9$ candies were distributed to 7 people, each person could have received $3 q+1$ candies, accounting for $21 q+7$ candies in total, with 2 candies left over.

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