Question

Brandy and Jennifer are selling wrapping paper for a school fundraiser.

Customers can buy rolls of plain wrapping paper and rolls of holiday wrapping paper. Brandy sold 2 rolls of plain wrapping paper and 1 roll of holiday wrapping paper for a total​ of​ $43. Jennifer sold 7 rolls of plain wrapping paper and 1 roll of holiday wrapping paper for a total​ of​ $93. Write a system of Linear Equations and find how much each type of wrapping paper costs per roll​ algebraically​

Answer 1

• Plain Wrapping Paper : $10
• Holiday Wrapping Paper : $23

Explanation:

Let :

• Plain wrapping paper = x
• Holiday wrapping paper = y

Equations

• 2x + y = 43 (Equation 1)
• 7x + y = 93 (Equation 2)

Subtract : (2) - (1)

• 7x + y - 2x - y = 93 - 43
• 5x = 50
• x = 10

Finding y

• 2(10) + y = 43
• 20 + y = 43
• y = 23

Plain Wrapping Paper : $10

Holiday Wrapping Paper : $23

Answer 2

Cost per roll of plain wrapping paper = $10

Cost per roll of holiday wrapping paper = $23

Explanation:

Let p = cost of a roll of plain wrapping paper

Let h = cost of a roll of holiday wrapping paper

Given:

• Brandy sold 2 rolls of plain wrapping paper and 1 roll of holiday wrapping paper for a total​ of​ $43

⇒ 2p + h = 43

Given:

• Jennifer sold 7 rolls of plain wrapping paper and 1 roll of holiday wrapping paper for a total​ of​ $93

⇒ 7p + h = 93

System of Linear Equations

Equation 1: 2p + h = 43

Equation 2: 7p + h = 93

To solve, subtract Equation 1 from Equation 2 to eliminate h:

⇒ 5p = 50

⇒ 5p ÷ 5 = 50 ÷ 5

⇒ p = 10

Substitute found value of p into Equation 1 and solve for h:

⇒ 2(10) + h = 43

⇒ 20 + h = 43

⇒ 20 + h - 20 = 43 - 20

⇒ h = 23

Cost per roll of plain wrapping paper = $10

Cost per roll of holiday wrapping paper = $23