Question

An animal shelter spends $4.00 per day to care for each cat and $4.50 per day to care for each dog. Gabriella noticed that the shelter spent $147.00 caring for cats and dogs on Wednesday. Gabriella found a record showing that there were a total of 35 cats and dogs on Wednesday. How many cats were at the shelter on Wednesday?

Answer 1

21 cats

Explanation:

Since there are two variables and two sets of data, you can set up a system of equations and use the method of subsitution to solve for a variable which can then be substituted into the other equation.

First equation: 4c + 4.5d = 147 where c = cats and d = dogs

Second equation: c + d = 35

Solve for d in the second equation: d = 35 - c

Substitute the expression '35 - c' in for 'd' in the first equation:

4c + 4.5(35 - c) = 147

Distribute: 4c + 157.7 - 4.5c = 147 or 157.5 - 0.5c = 147

Subtract 157.5 from both sides: 157.5 - 157.5 - 0.5c = 147 - 157.5 or -0.5c = -10.5

Divide and solve for c: -0.5c/-0.5 = -10.5/-0.5 or c = 21 cats