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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Comments
Aw - this one was OK. It is more easily done without algebra. Assume all 22 were boys = 44 legs. Each boy that is replaced by a dog equals 2 extra legs and we need 24 extra legs. So 12 dogs are needed.
I did the same as jimbo, but started with all dogs and changed to children. By the way, about the last bit of the solution, LOL!
i started out the same as jimbo, but then i changed course. i can't really explain what i did, i just got the right answer. and that made me feel good, cause some of the other teasers make me feel like a total moron...LoL
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