Question

An animal shelter spends $2.35 per day to care for each cat and $5.50 per day to care for each

dog. Pat noticed that the shelter spent $89.50 caring for cats and dogs on Wednesday.
Write an equation to represent the possible numbers of cats and dogs that could have been at the
shelter on Wednesday.
Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat’s
numbers possible? Use your equation to justify your answer.
Later, Pat found a record showing that there were a total of 22 cats and dogs at the shelter on
Wednesday. How many cats were at the shelter on Wednesday?

Answer 1

Ok, so we must set of a system of equations; however, we must check if Pat is correct first. All of the money goes into one equation and all of the pets go into the second.

x = cats, y = dogs

2.35x + 5.50y = 89.50
- plug in Pat’s statement

2.35(8) + 5.50(14) = 89.50

18.80 + 77 = 89.50
- 18.80 - 18.80

77 ≠ 70.70

So Pat is not correct.... Now let’s make the whole system....

2.35x + 5.50y = 89.50
x + y = 22

We can solve this with many methods, but substitution seems to be a bit more difficult, so we can use elimination...

whole system....

2.35x + 5.50y = 89.50
x(-2.35)+ y(-2.35) = 22(-2.35)

2.35x + 5.50y = 89.50
-2.35x - 2.35y = -51.70

- Add both equations together

3.15y = 37.8
y = 12

So there are twelve dogs; however, our problem is not solved. Let’s plug 12 back into the second equation to find the number of cats.

x + 12 = 22
- 12 - 12

x = 10

And there you have it! The shelter has 10 cats. You can always plug in x = 10 and y = 12 into one of the equations to check your work.