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  Number & Math Play

Two Legs, Four Legs		  
Q A puzzle maker looks out a window into his back yard. He sees a mix of boys and cats. He counts 22 heads and 68 legs. He wants YOU to figure out how many boys are in the yard.


  
A The boys plus the cats have a total of 22 heads. Or B + C = 22. Subtracting C from each side of the preceding results in a value for B of 22 - C.

The boys' legs equal two times the number of boys, the cats' legs equal four times the number of cats, and the total number of legs equals 68. Or 2B + 4C = 68. Using the value for B already calculated, the last equation can be rewritten as 2 (22 - C) + 4C = 68, or 44 - 2C + 4C = 68, which, by addition and subtraction, becomes 2C = 24, or C = 12.

There are 12 cats and 10 boys in the back yard.

From a puzzle inPuzzles, Patterns, and Pastimes: From the World of Mathematicsby Charles F. Linn. Garden City: Doubleday, 1969.