Question

Shreya and Shanice are selling pies for a

school fundraiser. Customers can buy
blueberry pies and lemon meringue pies.
Shreya sold 4 blueberry pies and 2 lemon
meringue pies for a total of $76. Shanice
sold 4 blueberry pies and 13 lemon
meringue pies for a total of $230. What is
the cost each of one blueberry pie and
one lemon meringue pie?

Answer 1

$26

Explanation:

Let blueberry pies = x and lemon pies = y.

4x + 13y = 230

4x + 2y = 76

Using elimination, we see that 11y = 154. Therefore, y = 14.

4x + 2(14) = 76

4x + 28 = 76

4x = 48

x = 12

x + y = 12 + 14 = 26.

$26 is your answer.

Answer 2

Explanation:

Let B be the price of a blueberry pie. Let L be the price of a lemon meringue pie.

We are told that Shreya makes a total of $76 by selling 4 blueberry and 2 lemon meringue pies. This can be made into an equation:

Shreya: 4B + 2L = $76

We also learn that Shanice is doing particularly well:

Shanice: 4B + 13L = $320

We want to determine the prices for each type of pie, B and L. We have two equations and two unknowns. That means we should be able to find the answers by substitution.

Rearrange Shreya's equation to isolate B:

Shreya: 4B + 2L = $76

4B = $76 - 2L

B = ($76-2L)/4

Now use this definition of B in Shanice's equation:

Shanice: 4B + 13L = $320

4( ($76-2L)/4) + 13L = $320

($76-2L) + 13L = $320

11L = 244

L = $22.18

Use L = $22.18 in either equation and solve for B:

4B + 2L = $76

4B + 2*($22.18) = $76

4B = $31.64

B = $7.91

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Blueberry pies are $7.91 each.

Lemon meringue pies are $22.18 each

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CHECK: Do these prices provide the correct sales for each person?

Price($/pie) Shreya Shanice

Blueberry 7.91 4 4

Lemon Mer. 22.18 2 13

Blueberry Sales ($) 31.64 31.64

Lemon Mer. Sales ($) 44.3 288.36

Total Sales $76 $320

YES - These prices account for each person's sales.