Find the price of each item being sold

Question

At a fund raising event, a booth was set up to sell handmade cards and photo frames. On the first day, 3 cards and 9 photo frames were sold for a total of $75. The next day, 8 cards and 5 photo frames were sold for a total of $67. Find the selling price of a card and the selling price of a photo frame. 

Answer 1

Let's solve this problem as a system of equations.

If we let C be a variable representing the price of one card and F be a variable representing the price of a photo frame, we can write two equations with these two variables.

 

First:

3C + 9F = 75

We can say this because the $75 sold came from 3 times the price of a card and 9 times the price of a photo frame.

 

And second:

8C + 5F = 67

using the same logic as above

 

One way to solve this system of equations is by using substitution. From the first equation, 

3C + 9F = 75

3C = 75 - 9F

C = 25 - 3F

 

Now we know that C = 25 - 3F, so let's plug that in to the second equation:

 

8C + 5F = 67

8(25 - 3F) + 5F = 67

200 - 24F + 5F = 67

-19F = -133

F = 7

 

We have found the price of a picture frame to be $7.

Additionally, we have solved for C as a function of F:

 

C = 25 - 3F

C = 25 - 3(7)

C = 4

 

A card costs $4 and a picture frame costs $7.