A pet store currently has a total of 45 cats and dogs. There are 7 more cats than dogs. How do you find the number of cats and dogs in the store?

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Answer 1 · 2016-11-20T12:06:46

In the store there are currently 19 dogs and 26 cats.

We are looking for the number of cats and dogs so let's call $c$ $c$ the number of cats and $d$ $d$ the number of dogs.

Now we are told there are 7 more cats ( $c$ $c$ ) than dogs ( $d$ $d$ ) so we can write this in mathematical terms as:

$c = d + 7$ $c = d + 7$

We are also told there is a total of 45 cats ( $c$ $c$ ) and dogs ( $d$ $d$ ). So we can write this as:

$c + d = 45$ $c + d = 45$

We can now substitute, from the first equation, $d + 7$ $d + 7$ for $c$ $c$ in the second equation and solve for $d$ $d$ :

$(d + 7) + d = 45$ $(d + 7) + d = 45$

$d + 7 + d = 45$ $d + 7 + d = 45$

$2 d + 7 = 45$ $2d + 7 = 45$

$2 d + 7 - 7 = 45 - 7$ $2d + 7 - 7 = 45 - 7$

$2 d = 38$ $2d = 38$

$\frac{2 d}{2} = \frac{38}{2}$ $(2d)/2 = 38/2$

$d = 19$ $d = 19$

Now that we have $d$ $d$ , or the number of dogs, we can substitute this back into the first equation to calculate $c$ $c$ , or the number of cats:

$c = 19 + 7$ $c = 19 + 7$

$c = 26$ $c = 26$