Question

Mr. Smith has a lot of cats and parrots and is not sure how many of each. He knows that last year for winter he bought a total of 31 hats for his pets. He also bought them a total of 96 shoes. How many cats does Mr. Smith have?

Answer 1

Given:

The total number of hats, h=31.

The total number of shoes, s=96.

Let c be the number of cats and p be the number of parrots.

Hence, the expression for the total number of hats can be written as,

`h=c+p\text{ ---(1)}`

A cat has 4 legs. So, the total number of shoes for cats is 4c.

A parrot has 2 legs. So, the total number of shoes for parrots is 2p.

Now, the expression for the total number of shoes can be written as,

`s=4c+2p\text{ ---(2)}`

Multiply equation (1) by 2.

`2h=2c+2p\text{ ---(3)}`

Now, subtract equation (3) from equation (2).

`\begin{gathered} s-2h=4c-2c \\ s-2h=2c \\ c=(s-2h)/(2) \end{gathered}`

Substitute the known values in the above equation to find the number of cats c.

`\begin{gathered} c=(96-2*31)/(2) \\ =(96-62)/(2) \\ =(34)/(2) \\ =17 \end{gathered}`

Therefore, the number of cats Smith has is 17.