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

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!

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