Question

A farmer's market sells pecans, walnuts, and cashews. They each have a

different cost and are priced per pound. Alyssa buys three pounds of walnuts
and four pounds of cashews and spends $32. Landon buys seven pounds of
pecans and five pounds of walnuts and spends $65. Tina buys 3 pounds of
pecans and 2 pounds of cashews and spends $22. Find the missing quantity
below.
D
Price per pound for Pecans = $

Answer 1

Price per pound for Pecans = $5

Explanation:

Let price per pound of walnut be x, price per pound of pecans be y and price per pound of cashew be z.

Thus;

For alyssa;

3x + 4z = 32 - - - (eq 1)

For Landon:

5x + 7y = 65 - - - (eq 2)

For Tina;

3y + 2z = 22 - - -(eq 3)

From eq 3, let's make z the subject;

z = (22 - 3y)/2

Putting this for z in eq 1 gives;

3x + 4((22 - 3y)/2) = 32

3x + 2(22 - 3y) = 32

3x + 44 - 6y = 32

3x - 6y = -12

Divide through by 3 to get;

x - 2y = -4 - - - eq(4)

Multiply through by -5 to give;

-5x + 10y = 20

Add this to eq 2 to get:

5x - 5x + 7y + 10y = 65 + 20

17y = 85

y = 85/17

y = 5

Thus, Price per pound for Pecans = $5