Please help me find the equation to solve this

Question

An animal shelter spends $1.50 per day to care for each cat and $6.50 per day to care for each dog. Gavin noticed that the shelter spent $97.00 caring for cats and dogs on Monday. Gavin found a record showing that there were a total of 18 cats and dogs on Monday. How many cats were at the shelter on Monday?

Answer 1

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!

Answer 2

let c = cats and d= dogs

This means a first equation demonstrating the price can be written as:

1.5c +6.5d =97

A second equation can be written demonstrating the total number of dogs and cats:

c + d = 18

or

d = 18-c

Now simply plug in 18-c for d in the first equation:

1.5c + 6.5(18-c) = 97

1.5c + 117-6.5c = 97

-5c = -10

c = 2

Therefore there were 2 cats at the shelter on Monday, and 16 dogs, since the total was 18.