Write a system of equations to represent the situation

Question

Mary and Nate are selling pies for a school fundraiser. Customers can buy cherry pies and blueberry pies. Mary sold 1 cherry pie and 1 blueberry pie for a total of $21. Nate sold 8 cherry pies and 2 blueberry pies for a total of $96. Find the cost of one cherry pie and one blueberry pie.

Answer 1

If use substitution instead of elimination, here's how.

x + y = 21, so x = 21 - y

8x + 2y = 96 → 8(21 - y) + 2y = 96

168 - 8y + 2y = 96

-6y = -72 → y = 12; x = 9

Answer 2

Hi Charles C

Cherry pies cost $9.00 each

Blueberry pies cost $12.00 each

We have two unknowns the price of Cherry Pies and Blueberry pies

Let x = Price of Cherry Pies

Let y = Price of Blueberry Pies

Mary sold one Cherry pie and one Blueberry pie for 21 dollars so Mary’s sale can be represented by

x + y = 21

Nate sold 8 Cherry pies and 2 Blueberry pies for 96 dollars so Nate’s sale can be represented by

8x + 2y = 96

Now we have two equations for our two unknowns which can be solved for by Elimination or Substitution. I will use Elimination.

x + y = 21

8x + 2y = 96

I will multiply Mary’s sale by -2, then add it to Nate’s sale to eliminate y

-2x - 2y = - 42

8x + 2y = 96

6x = 54

Divide both sides by 6

x = 9

Plug this x into Mary’s original sale to solve for y

x + y = 21

9 + y = 21

Subtract 9 from both sides

y = 21 - 9

y = 12

Use Nate’s sale to check

8(9) + 2(12)= 72 + 24 =96

Hope this helps you can try by substitution as well if you have any questions just ask.