I need help word problems

Question

An animal shelter spends $1.50 per day to care for each cat and $4.50 per day to care for each dog. Easton noticed that the shelter spent $52.50 caring for cats and dogs on Wednesday. Easton found a record showing that there were a total of 23 cats and dogs on Wednesday. How many cats were at the shelter on Wednesday?

Answer 1

Let's assume there were x cats and y dogs on Wednesday.

Since there were 23 total cats and dogs, x+y = 23, or we can re-write this as x = 23-y

Amount spent on cat on Wednesday = 1.5 * x

Amount spent on dog on Wednesday = 4.5 * y

Total amount spent on cat and dog on Wednesday = 1.5x + 4.5 y

From the above statement, 1.5x + 4.5y = 52.5 (since total amount spend on Wednesday was 52.5)

Substituting x (as x= 23-y as stated above), in the above equation,

1.5 (23-y) + 4.5y = 52.5, or 34.5 - 1.5y + 4.5 y = 52.5, or 3y = 18, or y = 6

Then x = 23-y or x = 23-6 = 17

Therefore there were 6 dogs and 17 cats on Wednesday.