An animal shelter spends $2.50 per day to care for each cat and $4.50 per day to care for each dog. Aaron noticed that the shelter spent $46.50 caring for cats and dogs on Thursday. Aaron found a record showing that there were a total of 13 cats and dogs on Thursday. How many cats were at the shelter on Thursday?

Write a system of governing equations:

c + d = 13

$2.50c + $4.50d = $46.50

c + d = 13 can be solved for either c or d. Solving for c, c = 13-d. Subst. 13-d into the second equation, replacing c:

$2.50 (13-d) + $4.50d = $46.50

32.5 - 2.5d + 4.5d = 46.50

Mult all terms by 100 to eliminate the decimal fractions:

3250 - 250d + 450d = 4650

Combine the d terms on the left, and move that 3250 to the right:

200d = 1400

Then d = 1400/200 = 7

There were 7 dogs and 13-7 cats, that is, 7 dogs and 6 cats.