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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​

Respuesta :

Answer:

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

Step-by-step 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

semsee45

Answer:

Cost per roll of plain wrapping paper = $10

Cost per roll of holiday wrapping paper = $23

Step-by-step 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

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