An animal shelter spends $5.50 per day to care for each cat and $8.00 per day to care for each dog. Owen noticed that the shelter spent $191.50 caring for cats and dogs on wednesday. How many cats were at the shelter on wednesday?

13, if 28 cats & dogs

Step-by-step explanation:

let c be the no. of cats and d be the no. of dogs

5.50c + 8d = 191.50

Notice that the sum is in 0.5, which is only possible when c is odd.

Try different combinations of c being odd and check which one gives d as a whole number, using

d = (191.50-5.50c) / 8

c = 1, d = [191.50-5.50 (1) ]/8

d = 23.25 (not possible)

c = 3, d = [191.50-5.50 (3) ]/8

d = 21.875 (not possible)

c = 5, d = [191.50-5.50 (5) ]/8

d = 20.5 (not possible)

c = 7, d = [191.50-5.50 (7) ]/8

d = 19.125 (not possible)

c = 9, d = [191.50-5.50 (9) ]/8

d = 17.75 (not possible)

c = 11, d = [191.50-5.50 (11) ]/8

d = 16.375 (not possible)

c = 13, d = [191.50-5.50 (13) ]/8

d = 15 (possible)

So c = 13 and d = 15