### Brain Teasers

# Boys and Dogs

Mad Ade has been asked to judge a dog show. He sees a mix of boys and dogs, and counts 22 heads and 68 legs. How many boys and dogs are at the show?

### Answer

The boys plus the dogs have a total of 22 heads, or B + D = 22. Subtracting D from each side of the preceding results in a value for B of 22 - D.The boys' legs equal two times the number of boys, the dogs' legs equal four times the number of dogs, and the total number of legs equals 68, or 2B + 4D = 68.

Using the value for B already calculated, the last equation can be rewritten as 2 (22 - D) + 4D = 68, or 44 - 2D + 4D = 68, which, by addition and subtraction, becomes 2D = 24, or D = 12.

There are 12 dogs and 10 boys in the show. Mad Ade eventually awarded first prize to the hotdog he had for lunch.

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