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).

$\begin{gathered} s-2h=4c-2c \\ s-2h=2c \\ c=\frac{s-2h}{2} \end{gathered}$

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

$\begin{gathered} c=\frac{96-2\times31}{2} \\ =\frac{96-62}{2} \\ =\frac{34}{2} \\ =17 \end{gathered}$

Therefore, the number of cats Smith has is 17.