# math

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A carpenter can make some chairs and stools. All together there are 32 legs. If the carpenter has pieces of wood that can be used to make 9 seats, how many chairs and how many stools can a carpenter make?

• math -

The problem with this question is that it does not define how many legs on a chair or a stool. So let us start by defining that a chair has 4 legs and a stool has 3 legs. The chair I am sitting on has 5 legs and the stool in the room as 4 legs so this is not a given.

We can thus come up with two equations.

If there are C chairs and S stools, the number of legs must equal 32 so

4C+3S=32

also the total number of seats equals 9, and as each has a seat, then

C+S=9

we can solve these for C and S

I got S=4 and C=5

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