Question

An animal shelter spends $1.00 per day to care for each cat and $7.00 per day

to care for each dog. Claire noticed that the shelter spent $135.00 caring for
cats and dogs on Thursday. Claire found a record showing that there were a
total of 39 cats and dogs on Thursday. How many cats were at the shelter on
Thursday?

Answer 1

23 cats

Explanation:

let x be the number of cats at the shelter on Thursday

and let y be the number of dogs at the shelter on Thursday.

Now we have two unknown variable x and y so we need at least two equations to solve for both x and y.

The first equation can be written from the statement "total of 39 cats and dogs on Thursday", which converts to :

x+y=39

The second equation can be determined from the sentence "the shelter spent $135.00 caring for cats and dogs on Thursday" . Also we know that the shelter spends $1/day for cats and $7/day for dogs which means 1*x (as x is the total number of cats) and 7*y (as y is the total number of dogs on Thursday) and we also know that the shelter spend a total of $135 which means that:

1x+7y=135

Now from first equation we can find the value of x which is x=39-y and then we replace this value of x in the second equation and solve for y.

1(39-y)+7y=135

39+6y=135

6y=135/39

6y=96

y=96/6

y=16

Now to find x (the number of cats on Thursday), we put this value of y in the first equation which gives us:

x=39-16

x=23