Olympiad Maths Prep

Track / Stage 5 / 145 of 400 #745 of 2000

Problem 745

AIME late
Algebra Difficulty 5.3 Find the answer

Bakayev E.V.

Father Frost distributed 47 chocolates to the children in such a way that each girl received one more chocolate than each boy. Then Father Frost distributed 74 jelly candies to the same children in such a way that each boy received one more jelly candy than each girl. How many children were there in total?

Official solution

A total of 121 sweets were distributed, and all children received an equal share. This means the number of children is a divisor of 121, that is, 1, 11, or 121.

The first case is obviously not suitable. In the second case, 8 boys received 4 chocolates and 7 jelly candies each, and 3 girls received 5 chocolates and 6 jelly candies each. In the third case, 47 girls received one chocolate each, and 74 boys received one jelly candy each.

## Otвет

11 or 121.

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