Question

Jose and Jill are selling pies for a school fundraiser. Customers can buy cherry pies and lemon meringue pies. Jose sold 17 cherry pies and 14 lemon meringue for a total of $321. Jill sold 9 cherry pies and 5 lemon meringue pies for a total of $141. Find the cost of one cherry pie and one lemon meringue pie.

Answer 1

Cost of one cherry pie is $ 9 and cost of one lemon meringue is $ 12

Solution:

Let "c" be the cost of one cherry pie

Let "m" be the cost of one lemon meringue

Given that Jose sold 17 cherry pies and 14 lemon meringue for a total of $321

We can frame a equation as:

17 cherry pies x cost of one cherry pie + 14 lemon meringue x cost of one lemon meringue = $ 321

$17 \times c + 14 \times m= 321$

17c + 14m = 321 ------- eqn 1

Jill sold 9 cherry pies and 5 lemon meringue pies for a total of $141

9 cherry pies x cost of one cherry pie + 5 lemon meringue x  cost of one lemon meringue = $ 141

$9 \times c + 5 \times m = 141$

9c + 5m = 141  -------- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "c" and "m"

Multiply eqn 1 by 5

85c + 70m = 1605 ----- eqn 3

Multiply eqn 2 by 14

126c + 70m = 1974  ------- eqn 4

Subtract eqn 3 from eqn 4

126c + 70m = 1974

85c + 70m = 1605

(-) -------------------

41c = 369

c = 9

Substitute c = 9 in eqn 1

17c + 14m = 321

17(9) + 14m = 321

14m = 369 - 153

14m = 168

m = 12

Thus the cost of one cherry pie is $ 9 and cost of one lemon meringue is $ 12