Question

Bill and abhasra are selling pies for a school fundraiser. Customers can buy blueberry pies and black berry pies. Bill sold 12 blueberry pies and 9 blackberry pies for a total of $324. Abhasra sold 6 blueberry pies and 12 blackberry pies for a total of $312. What is the cost each of one blueberry pie and one blackberry pie?

Answer 1

I set up a system of equations to solve this problem.

Answer 2

Blueberry will be represented with variable x
Blackberry will be represented with variable Y

There will be two equations

First one: Bill sold 12 blueberry and 9 blackberry for $324 total.
Equation: 12x + 9y = 324

Second one: Abhasra sold 6 blueberry and 12 blackberry for $312. Equation: 6x + 12y = 312

Use elimination by adding.

12x + 9y = 324
6x + 12y = 312

To eliminate by adding, one of the variable values , example : both x, have to have same coefficients with one positive and the other negative, so multiply the bottom equation by negative 2.

-2(6x + 12y = 312) =
-12x -24y = -624

Now add both equations

12x + 9y = 324
(+)-12x - 24y = -624
-15y = - 300

Now divide both sides by -15 to isolate variable y
y = 20 .
Now that you have the amount of y, to find x, take one of the equations and replace the y value with 20.

12x + 9(20) = 324
Multiply
12x + 180 = 324
Subtract 180 from both sides
12x = 144
Divide 12 by both sides to isolate x
x = 12

Each blueberry pie costs $12 and each blackberry pie costs $20