Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. Mrs. Shepherd's grandchildren are participating in a gift wrap sale to raise money for their school. She decided to stock up, so she ordered 2 rolls of reversible paper and 5 rolls of metallic paper from Valeria, spending a total of $90. She also ordered 4 rolls of reversible paper and 5 rolls of metallic paper from Jill, which cost a total of $120. Assuming that rolls of each type are priced the same, what is the price for each kind of paper? Rolls of reversible paper cost $_____ each, and rolls of metallic paper cost $_____ each.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  Mrs. Shepherd's grandchildren are participating in a gift wrap sale to raise money for their school. She decided to stock up, so she ordered 2 rolls of reversible paper and  5 rolls of metallic paper from Valeria, spending a total of $90. She also ordered 4 rolls of reversible paper and  5 rolls of metallic paper from Jill, which cost a total of $120. Assuming that rolls of each type are priced the same, what is the price for each kind of paper?  Rolls of reversible paper cost $_____ each, and rolls of metallic paper cost $_____ each.

Bytelearn · Accepted Answer

Define variables: Define the variables for the cost of each type of paper. Let x be the cost of one roll of reversible paper, and y be the cost of one roll of metallic paper.Write equations: Write the system of equations based on the given information. First order: 2 rolls of reversible paper and 5 rolls of metallic paper for $90. Second order: 4 rolls of reversible paper and 5 rolls of metallic paper for $120. The system of equations is: 2x + 5y = 90 4x + 5y = 120Eliminate variable: Decide which variable to eliminate. We can eliminate y because it has the same coefficient in both equations.Subtract equations: Subtract the first equation from the second to eliminate y. (4x + 5y) - (2x + 5y) = 120 - 90 4x + 5y - 2x - 5y = 120 - 90 2x = 30Solve for x: Solve for x. 2x = 30 x = 30 / 2 x = 15Substitute x: Substitute the value of x into one of the original equations to solve for y. Using the first equation: 2x + 5y = 90 2(15) + 5y = 90 30 + 5y = 90 5y = 90 - 30 5y = 60 y = 60 / 5 y = 12Check solution: Check the solution by substituting both values into the second equation. 4x + 5y = 120 4(15) + 5(12) = 120 60 + 60 = 120 120 = 120 The solution checks out.

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