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?

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

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