Question

An animal shelter spends $5.50 per day to care for each cat and $7.00 per day to care for each dog. Ryan noticed that the shelter spent $52.50 caring for cats and dogs on Monday. Ryan found a record showing that there were a total of 9 cats and dogs on Monday. How many cats were at the shelter on Monday?

Answer 1

Answer: There were 7 cats at the shelter on Monday.

Explanation:

Hi, to answer this question we have to write a system of equations using the information given.

• c + d = 9 (there were a total of 9 cats (c) and dogs (d) on Monday)

• 5.50 c + 7 d = 52.50 (An animal shelter spends $5.50 per day to care for each cat and $7.00 per day to care for each dog)

Isolating d on the first equation:

d =9 -c

Replacing the value of d in the second equation

5.50 c + 7 d = 52.50

5.50 c + 7 (9-c) = 52.50

5.50c +7(9) -7(c) =52.50

5.50c +63 -7c =52.50

63 -52.50 = 7c-5.50c

10.5= 1.5c

10.5/1.5=c

c= 7

There were 7 cats at the shelter on Monday.

Feel free to ask for more if needed or if you did not understand something.

Answer 2

There were 7 cats

Explanation:

In this question, we are asked to calculate the number of individual cats and dogs present at an animal shelter on a certain Monday.

Since we do not know the exact numbers, let’s represent these animals by variables. Let the number of dogs be d and the number of cats be c .

Since there are a total of 9 animals, this means;

c + d = 9 •••••••••(I)

Let’s now get the second equation out of their finances;

Total amount spent on dogs will be 7 * d = 7d while total amount spent on cats will be 5.5 * c = 5.5c. If we add both, we will get the total amount spent which is $52.5

Mathematically therefore;

5.5c + 7d = 52.5 ••••••••(ii)

Now from 1, we can say that c = 9 - d

Let’s substitute this in ii

5.5(9-d) + 7d = 52.5

49.5 - 5.5d + 7d = 52.5

1.5d = 52.5 - 49.5

1.5d = 3

d = 3/1.5 = 2

Since d = 2, c = 9 - d = 9 - 2 = 7