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Question

An animal shelter spends $2.50 per day to care for each cat and $7.50 per day to care for each dog. Brandon noticed that the shelter spent $182.50 caring for cats and dogs on Thursday. Brandon found a record showing that there were a total of 37 cats and dogs on Thursday. How many cats were at the shelter on Thursday?

Answer 1

Let's let c represent the NUMBER of cats at the shelter on Thursday and d represent the NUMBER of dogs. Since there are a total of 37 animals , we can write:

c + d = 37

Then since it costs $2.50 a day for each cat and $7.50 per day for each dog, we can represent the total money spent by:

2.50c + 7.50d = $182.50

To solve these two equations with two unknowns, use substitution.

From the first equation we can write that c = 37 - d

Substitute this expression for c into the second equation:

2.50c + 7.50d = 182.50

2.50 (37 - d ) + 7.50d = 182.50

Solve for d using inverses operations, combining like terms, and the distributive property :

92.50 - 2.50d + 7.50d = 182.50

92.50 + 5d = 182.50

92.50 + 5d - 92.50 = 182.50 - 92.50

5d = 90

5d / 5 = 90 / 5

d = 18 dogs

Then for the number of cats: c + d =37

c + 18 = 37

c = 19 cats