Question 1058466: Kylie was buying pies at the store for her co-workers on Thanksgiving. She needs a total of 12 pies. The store sells pumpkin pies for $4 a pie and apple pies for $2 a pie. If Kylie ended up spending $30 on pies alone, how many of each pie did she purchased?
1. Write and solve a systems of equations representing this situation.
2. If Kylie wanted to add two pecan pies to her order for $1 each and maintain the same total cost, how much of each pie does she end up getting?
Checking my answer for this, I created it myself. Could you show the steps in solving this?
Answer by solve_for_x(190)   (Show Source):
You can put this solution on YOUR website! Let x represent the number of pumpkin pies that Kylie buys, and let y represent the number of apple pies.
The total number of pies purchased is x + y = 12
The total cost is 4x + 2y = 30
Solving the the first equation for y gives:
y = 12 - x
Substituting "12 - x" in place of y in the equation 4x + 2y = 30 gives:
4x + 2(12 - x) = 30
4x + 24 - 2x = 30
2x + 24 = 30
2x = 6
x = 3
Thus, she has purchased 3 pumpkin pies, and 12 - 3 = 9 apple pies.
If Kylie wishes to purchase two pecan pies at a cost of $1 each, that would add $2
to the total cost. Since Kylie wants to keep the same total price, the quantity of
pumpkin and apple pies must be reduced by $2. The only way to do this is to
remove one apple pie from the original order.
The new order would be 3 pumpkin pies, 8 apple pies, and 2 pecan pies.
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