Kaitlyn E. answered • 7d

Let me help you learn

So let's first start by creating variables to represent the number of cats and number of dogs.

Number of cats = x

Number of dogs = y

This means that the total cost of caring for cats would be the price of caring for one cat ($1.50) multiplied by the number of cats (x).

$1.5x = total cost of cats

Using the same process for dogs, the total price of caring for dogs is given by the equation:

$6.5 = total cost of cats and dogs

The problem tells us first that $97 is the total cost of caring for dogs and cats together.

So we have the equation:

$97 = total cost of dogs + total cost of cats. (1)

We substitute the two equations in for the total costs to get:

$97= $6.5y + $1.5x. (2)

Now we have two variables x and y. But the problem also tells us the sum of cats and dogs. We know:

x+y=18

Rearranging this gives us: y= 18-x

Subsituting 18-x for y in equation 2 gives us:

$97= $6.5(18-x) + $1.5x

Now solving this equation for x would give is the number of cats. We can use that to find the number of dogs. I hope this helps!