Answer:
There were 9 cats at the shelter on Wednesday.
Step-by-step 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 [tex]x[/tex].
And let the number of dogs be [tex]y[/tex].
So, total number of dogs:
[tex]x+y=34.[/tex]
[tex]y=34-x.[/tex]......( 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:
[tex]3x+5.50y=164.50[/tex]
Putting the value of equation ( 1 ) in the place of [tex]y[/tex] :
⇒ [tex]3x+5.50(34-x)=164.50[/tex]
⇒ [tex]3x+187-5.50x=164.50[/tex]
⇒ [tex]187-2.50x=164.50[/tex]
Adding [tex]2.50x[/tex] on both the sides we get:
⇒ [tex]187=164.50+2.50x[/tex]
Subtracting 164.50 on both sides we get:
⇒ [tex]22.50=2.50x[/tex]
Dividing by 2.50 on both sides we get:
⇒ [tex]9=x[/tex]
⇒ [tex]x=9.[/tex]
The number of cats = 9.
Therefore, there were 9 cats at the shelter on Wednesday.
