Question

Part I: Arcelia Apple Pies. Arcelia plans to make apple pies for an upcoming fundraiser. She will make two types of apple pies, one type with mostly Granny Smith apples (more tart and less sugar) and another type with mostly Red Delicious apples (sweeter pies). She negotiates a great deal on apples from a local apple farm who gives her 50 Granny Smith apples and 70 Red Delicious apples. If each of the tart pies takes 4 Granny Smith apples and 2 Red Delicious and each of the sweet pies takes 5 Red Delicious apples and 1 Granny Smith apple, how many of each type of pie can she make? 1) Write two equations to use to solve for how many tart pies and how many sweet pies she can make from the supplies on hand. Let x be the number of tart pies made and y be the number of sweet pies made. 2.) Try to solve this system of equations. If you get a solution, state what it means in trems of the context of the problem. If not, describe what your result means.

Answer 1

1) 4x + y = 50

2x + 5y = 70

2) x = 10 tart pies and y = 10 sweet pies

This means that Arcelia can perfectly make 10 tart pies and 10 sweet pies with the ingredients she has.

Explanation:

- Let x be the number of tart pies made and y be the number of sweet pies made

- Each of the tart pies takes 4 Granny Smith apples and 2 Red Delicious apples.

- Each of the sweet pies takes 5 Red Delicious apples and 1 Granny Smith apple.

x tart pies would require 4x Granny Smith apples and 2x Red Delicious apples.

y sweet pies would require 5y Red Delicious apples and y Granny Smith apples.

Arcelia has 50 Granny Smith apples and 70 Red Delicious apples.

Hence,

4x + y = 50

2x + 5y = 70

Solving the simultaneous equation,

y = 50 - 4x

2x + 5y = 70

2x + 5(50 - 4x) = 70

2x + 250 - 20x = 70

18x = 180

x = 10

y = 50 - 4x = 50 - 40 = 10.

So, Arcelia can perfectly make 10 tart pies and 10 sweet pies with the ingredients she has.

Hope this Helps!!!