how do I do word problems with money

Question

Alberto and Sumalee are selling pies for a school fundraiser. Customers can buy cherry pies and blackberry pies. Alberto sold 8 cherry and 2 blackberry pies for a total of 74 dollars. Sumalee sold 3 cherry and 2 blackberry pies for a total of 44 dollars. What is the cost of one cherry pie and one blackberry pie?

Answer 1

Hi Jessica!

 

So, let's start by writing this problem out as two equations. I'll use the variable "c" for cherry pies and "b" for blackberry pies.

 

8c + 2b = 74

3c + 2b = 44

 

The next thing to do is solve for one of the variables. Let's take the first equation and solve for b.

 

8c + 2b = 74

-8c          -8c

 

2b = 74 - 8c

/2        /2

 

b = 37 - 4c

 

Now that we have a value for b, let's substitute it in the second equation to find a value for c.

 

3c + 2(37 - 4c) = 44

3c + 74 - 8c = 44

74 - 5c = 44

-74         -74

 

-5c = -30

-1(-5c = -30)

5c = 30

/5    /5

 

c = 6

 

Now, we have a numerical value for c! Plug that value into either equation to find the value for b.

 

8(6) + 2b = 74

48 +2b =74

-48       -48

 

2b = 26

/2     /2

 

b = 13

 

Finally, plug the numbers in both equations to make sure you're correct.

 

8(6) + 2(13) = 74

48 + 26 =74

74 = 74 

 

3(6) + 2(13) = 44

18 + 26 = 44

44 = 44

 

And that's it! So: cherry pies cost $6 and blackberry pies cost $13.