Answer:
The number of cats are 23 and the number of dogs are 10 at the shelter on tuesday .
Step-by-step 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
[tex]\frac{150x}{100}+\frac{850y}{100}= \frac{11950}{100}[/tex]
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
[tex]y = \frac{7000}{700}[/tex]
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 .
