An animal shelter spends $5.00 per day to care for each cat and $8.50 per day to care for each dog. isaac noticed that the shelter spent $248.50 caring for cats and dogs on thursday. isaac found a record showing that there were a total of 35 cats and dogs on thursday. how many cats were at the shelter on thursday?

There are 21 dogs calculated as follows:
Let x represent number of cats, and y represent number of dogs.
On Thursday, there are a total of 35 cats and dogs, so:
x + y = 35 Equation (1)
The shelter spends $ per cat, so total expense for cats is $5x. Similarly, the expense for dogs would be $8.5y.
The total expense for 35 cats and dogs for Thursday is $248.50, so:
5x + 8.5y = $248.50 Equation (2)
Multiplying Equation (1) by 50 and Equation (2) by 10 we have:
50x + 50y = 1750 Equation(3) and
50x + 85y = 2485 Equation (4).
Subtracting Equation (3) from Equation (4) gives:
35y = 735, therefore y = 735/35 = 21.
There are 35 cats and dogs, therefore the number of cats = 35 - 21 = 14
CHECK:
21 dogs @ $8.50 = $178.50
14 cats @ $5.00   = $70.00
Total = $248.50