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:
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!