There were 25 cats at the shelter on Friday.
The Breakdown
Assuming the number of cats at the shelter is represented by 'c' and the number of dogs is represented by 'd'.
According to the given information, the shelter spends $5.00 per day to care for each cat and $8.00 per day to care for each dog.
The total amount spent on cats can be calculated by multiplying the number of cats (c) by the cost per day ($5.00): 5c.
Similarly, the total amount spent on dogs can be calculated by multiplying the number of dogs (d) by the cost per day ($8.00): 8d.
We are also given that the shelter spent a total of $205.00 caring for cats and dogs on Friday. Therefore, we can set up the following equation:
5c + 8d = 205
We also know that the total number of cats and dogs on Friday was 35:
c + d = 35
To solve this system of equations, we can use substitution or elimination. Using the elimination method:
Multiply the second equation by 5 to make the coefficients of 'c' in both equations the same:
5(c + d) = 5(35)
5c + 5d = 175
Now, we can subtract the second equation from the first equation to eliminate 'c':
(5c + 8d) - (5c + 5d) = 205 - 175
3d = 30
Divide both sides of the equation by 3:
d = 10
Substitute the value of 'd' back into the second equation to find 'c':
c + 10 = 35
c = 35 - 10
c = 25
Therefore, there were 25 cats at the shelter on Friday.