Question

A local animal shelter needs your help with its budget. Last week, the shelter fed 20 cats

and 12 dogs, a feat that cost them $532. This week, the shelter fed 13 cats 9 dogs, which
cost them $371. How much does it cost the shelter to feed each cat for a week? Each
dog?

Answer 1

we can start by setting up two equations

let c=# of dollars it takes to feed a cat
let d=# of dollars it take to feed a dog

20c+12d=532
13c+9d=371

solving by elimination

the lowest common multiple between 9 and 12 is 36

60c+36d=1596
-52c-36d=-1484

8c=112
c=14

substitute 14 in to find d

13(14)+9y=371

d=21

it takes $14 to feed each cat and $21 to feed each dog