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Puzzle Details

A kind old gentleman decided to give 12 sweets to each of the girls in his town and 8 sweets to each of the boys.

Of the 612 children in his town, only half the girls and three quarters of the boys took the sweets.

How many sweets did the kind old gentleman have to buy?

The actual number of girls and boys doesn't actually matter!

If all of the children were girls then half of them (306) would be given 12 sweets:

306 x 12 = 3672

If all of the children were boys then three quarters of them (459) would be given 8 sweets:

459 x 8 = 3672

If there were 512 girls (so 256 would get 12 sweets = 3072) and 100 boys (so 75 would get 8 sweets = 600):

256 x 12 + 75 x 8 = 3672

We can change the numbers of girls and boys, but it doesn't change the answer. The reason for this lies in the fact that 1/2 girls x 12 sweets = 3/4 boys x 8 sweets (both are 6).

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