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?

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

To solve this problem, we can set up a system of equations.

Let's assume that the carpenter can make 'x' chairs and 'y' stools.

Each chair has 4 legs, and each stool has 3 legs. Since there are a total of 32 legs, we can write the equation:

4x + 3y = 32

We also know that the carpenter has enough wood to make 9 seats, which means the number of chairs and stools should add up to 9:

x + y = 9

We now have a system of two equations:

4x + 3y = 32
x + y = 9

We can solve this system by using a method like substitution or elimination. Let's use the elimination method here.

To eliminate 'y', we can multiply the second equation by 3:

3(x + y) = 3(9)
3x + 3y = 27

Now, we can subtract this equation from the first equation:

(4x + 3y) - (3x + 3y) = 32 - 27
x = 5

Substituting this value back into the second equation:

5 + y = 9
y = 9 - 5
y = 4

Therefore, the carpenter can make 5 chairs and 4 stools.