Question

An animal shelter spends $1.50 per day to care for each cat and $8.50 per day to care for each dog. Levi noticed that the shelter spent $119.50 caring for cats and dogs on Tuesday. Levi found a record showing that there were a total of 33 cats and dogs on Tuesday. How many cats were at the shelter on Tuesday?

Answer 1

The number of cats are 23 and the number of dogs are 10 at the shelter on tuesday .

Explanation:

Let us assume that the number of cats be x .

Let us assume that the number of dogs be y .

As given

An animal shelter spends $1.50 per day to care for each cat and $8.50 per day to care for each dog.

Levi noticed that the shelter spent $119.50 caring for cats and dogs on Tuesday.

Equation becomes

1.50x + 8.50y = 119.50

Simplify the above

`(150x)/(100)+(850y)/(100)= (11950)/(100)`

150x + 850y = 11950

Levi found a record showing that there were a total of 33 cats and dogs on Tuesday.

Equation becomes

x + y = 33

Two equations are

150x + 850y = 11950

x + y = 33

Multiply x + y = 33 by 150 and subtracted from 150x + 850y = 11950 .

150x - 150x + 850y - 150y = 11950 - 4950

700y = 7000

`y = (7000)/(700)`

y = 10

Putting value of y in the equation x + y = 33 .

x + 10 = 33

x = 33 - 10

x = 23

Therefore the number of cats are 23 and the number of dogs are 10 at the shelter on tuesday .