Question

An animal shelter spends $4.50 per day to care for each bird and $6.50 per day to

care for each cat. Ayden noticed that the shelter spent $183.00 caring for birds and
cats on Tuesday. Ayden found a record showing that there were a total of 34 birds
and cats on Tuesday. How many birds were at the shelter on Tuesday?​

Answer 1

15 birds

Explanation:

Substitition would be the best way to solve this because x and y have 1 as a coefficient, making this much easier on us.

First, let's set up a system of equations. The first equation represents the number of birds and cats, while the second one represents how much was spent on Tuesday.

x + y = 34

4.5x + 6.5y = 183

x represents the number of birds, while y represents the number of cats. First, let's isolate x on the first equation. The result will give us something we can solve the second equation with.

x + y = 34

To isolate x, subtract y from both sides.

x = 34 - y

We're going to solve this problem by substituting x with 34 - y. This'll give us only one variable in the equation, then we can solve from there.

4.5x + 6.5y = 183

Plug in 34 - y in place of x.

4.5(34 - y) + 6.5y = 183

Now distribute 4.5 to everything in parentheses.

153 - 4.5y + 6.5y = 183.

Simplify.

153 + 2y = 183

Subtract 153 from both sides.

2y = 30

Divide.

y = 15

And there's your answer! If you're required to check your solution, here's how to do it:

Choose one of your equations. The first one would be much easier.

x + y = 34

Plug in your y-value, 15, and solve for x.

x + 15 = 34

x = 19

Now plug both x and y back in. If the resulting equation is true, then your solution is correct.

19 + 15 = 34

34 = 34

The solution is correct!