Question

The school store sells pens, pencils, and paper. The pens are $1.25 each, the pencils are $0.50 each, and the paper is $2 per pack. Yesterday the store sold 25 items and earned $32. The number of pens sold equaled the number of pencils sold plus the number of packs of paper sold minus 5. Write the Equations that represent the situation.

Answer 1

x = 10, y = 7, z = 8

Pens = 10, pencils = 7, paper = 8

Explanation:

Pens = $1.25

Pencils = $0.50

Paper = $2

Total sales = 25

Total revenue= $32

Pens = x

Pencils = y

Paper = z

x + y + z = 25

1.25x + 0.50y + 2z = 32

The number of pens sold equaled the number of pencils sold plus the number of packs of paper sold minus 5

x = y + z - 5

Substitute x = y + z - 5 into the equation

y + z - 5 + y + z = 25

1.25(y + z - 5) + 0.50y + 2z = 32

2y + 2z - 5 = 25

1.25y + 1.25y - 6.25 + 0.50y + 2z = 32

2y + 2z = 25 + 5

1.75y + 3.2z = 32 + 6.25

2y + 2z = 30 (1)

1.75y + 3.25z = 38.25 (2)

Multiply (1) by 13 and (2) by 8

26y + 26z = 390

14y +26z = 306

Subtract

26y - 14y = 390 - 306

12y = 84

Divide both sides by 12

y = 84 / 12

= 7

Substitute y = 7 into (1)

2y + 2z = 30

2(7) + 2z = 30

14 + 2z = 30

2z = 30 - 14

2z = 16

z = 16 / 2

= 8

z = 8

Substitute y = 7, z = 8 into

x + y + z = 25

x + 7 + 8 = 25

x + 15 = 25

x = 25 - 15

= 10

x = 10

x = 10, y = 7, z = 8

Pens = 10, pencils = 7, paper = 8