A kind old person decided to give 12 sweets to each of the adults in the town and 8 sweets to each of the children.

Of the 612 people in the town, exactly half of the adults, and exactly three quarters of the children took the sweets.

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

Puzzle Copyright © Kevin Stone

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Hint

The number of adults and children doesn't matter.

Answer

3,672.

Reasoning

The actual number of adults and children doesn't actually matter.

If all of the people were adults, then half of them (306) would be given 12 sweets:

306 x 12 = 3672

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

459 x 8 = 3672

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

256 x 12 + 75 x 8 = 3672

We can change the numbers of adults and children, but it doesn't change the answer.

The reason for this lies in the fact that 1/2 adults x 12 sweets = 3/4 children x 8 sweets (both are 6).