Question

an animal shelter spends $3.00 per day for each cat and $5.50 per day for each dog. Nick noticed that the shelter spent $164.50 caring for cats and dogs on Wednesday. Nick found a record showing that there were a total of 34 cats and dogs on Wednesday. How many cats were at the shelter on Wednesday?​

Answer 1

There were 9 cats at the shelter on Wednesday.

Explanation:

Given:

An animal shelter spends $3.00 per day for each cat and $5.50 per day for each dog.

Nick noticed that the shelter spent $164.50 caring for cats and dogs on Wednesday.

Nick found a record showing that there were a total of 34 cats and dogs on Wednesday.

Now, to find the number of cats at the shelter on Wednesday.

Let the number of cats be
`x`.

And let the number of dogs be
`y`.

So, total number of dogs:

`x+y=34.`

`y=34-x.`......( 1 )

As given animal shelter spends $3.00 per day for each cat and $5.50 per day for each dog.

Now, total money animal shelter spent on Wednesday:

`3x+5.50y=164.50`

Putting the value of equation ( 1 ) in the place of
`y` :

⇒
`3x+5.50(34-x)=164.50`

⇒
`3x+187-5.50x=164.50`

⇒
`187-2.50x=164.50`

Adding
`2.50x` on both the sides we get:

⇒
`187=164.50+2.50x`

Subtracting 164.50 on both sides we get:

⇒
`22.50=2.50x`

Dividing by 2.50 on both sides we get:

⇒
`9=x`

⇒
`x=9.`

The number of cats = 9.

Therefore, there were 9 cats at the shelter on Wednesday.