An animal shelter spends $3.00 per day to care for each cat and $6.50 per day to care for each dog. amelia noticed that the shelter spent $84.00 caring for cats and dogs on friday. amelia found a record showing that there were a total of 21 cats and dogs on friday. how many cats were at the shelter on friday?

There were 15 cats at the shelter on Friday.

Step-by-step explanation:

Cost of caring each cat = $3.00

Cost for caring each dog = $6.50

Total money spent by shelter = $84.00

Total Cats and Dogs in the shelter = 21

Let the number of cats in the shelter = k

So, the number of dogs in shelter =  21 -k

Also according to the question:

Total expenditure on cats + total expenditure on dogs = $84.00

or, k ($3.00) + (21-k)($6.50)  = $84.00

or, 3k + 136.5 - 6.5 k = 84

or, -3.5 k = 84 - 136.5 = -52.5

⇒3.5 k = 52.5  or k = 52.5/3.5 = 15

⇒  k = 15

Hence, the number of cats in the shelter was 15 on Friday.