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

To find the cost of one cherry pie and one lemon meringue pie, we can set up a system of equations using the given information. Solving this system of equations, we find that the cost of one cherry pie is approximately $2.88 and the cost of one lemon meringue pie is approximately $19.43.

Step-by-step explanation:

To find the cost of one cherry pie and one lemon meringue pie, we need to set up a system of equations based on the information given.

Let's assume the cost of a cherry pie is x dollars and the cost of a lemon meringue pie is y dollars.

We can set up two equations using the given information:

Equation 1: 17x + 14y = 321

Equation 2: 9x + 5y = 141

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:

From Equation 1, we can express x in terms of y: x = (321 - 14y)/17

Substituting this expression for x into Equation 2, we get:

9((321 - 14y)/17) + 5y = 141

Simplifying the equation:

289 - (126/17)y + 5y = 141

285 - (126/17)y = 141

(126/17)y = 144

y = 144 * 17/126 = 19.43

Substituting the value of y into Equation 1, we can find the value of x:

17x + 14(19.43) = 321

17x + 272.02 = 321

17x = 48.98

x = 48.98/17 = 2.88

Therefore, the cost of one cherry pie is approximately $2.88 and the cost of one lemon meringue pie is approximately $19.43.

Answer 2

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 * c + 14 * 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 * c + 5 * 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