Please help me find the equations to solve this!

Question

An animal shelter spends $5.50 per day to care for each cat and $8.00 per day to care for each dog. Angel noticed that the shelter spent $54.00 caring for cats and dogs on Monday. Angel found a record showing that there were a total of 8 cats and dogs on Monday. How many cats were at the shelter on Monday?

Answer 1

This problem can be solved by setting up a simple system of equations.

Let the number of cats be c and number of dogs be d

The first equation demonstrates the total price:

5.5c +8d =54

The second equation demonstrates the total number of dogs and cats:

c+d = 8

Now that we have our two equations, we can solve using substitution.

d = 8-c

We can plug in 8-c for d in the first equation.

5.5c + 64 - 8c = 54

-2.5c = -10

c =4

Therefore, there were 4 cats in the store on Monday, and 4 dogs, since the total was 8.

Answer 2

Hi Kaleigh,

For word problems like this where you need to write and solve your own equations, the first step is to define what the variables should represent. As the question asks us how many cats were at the shelter on Monday, that gives us an idea on what our variables should represent.

Let x = the number of cats at the shelter on Monday.

Let y = the number of dogs at the shelter on Monday.

Now that our variables are defined, we can figure out how to write equations from the information.

With the costs associated with the animals, we can write the following equation:

5.50x + 8.00y = 54.00

As there were a total of 8 animals, we can write the equation:

x + y = 8

This is now your system of equations you can solve (using substitution, elimination, graphing, or matrices).

When you solve, you will find that there were 4 cats at the shelter on Monday. I hope this helps!

Answer 3

first, I will define my variables:

let c = number of cats cared for

let d = number of dogs cared for

since there are two unknown variables, you need two equations.

5.50c + 8.00d = 54

c + d = 8

There are many ways you can move forward from here. I’d recommend solving for c or d and substituting that into the other equation.

c = 8 - d

5.50(8 - d) + 8.00d = 54