Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

Mrs. Henson's grandchildren are participating in a gift wrap sale to raise money for their school. She decided to stock up, so she ordered 1 roll of reversible paper and 3 rolls of metallic paper from Peter, spending a total of $43. She also ordered 4 rolls of reversible paper and 4 rolls of metallic paper from Ron, which cost a total of $100. 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.

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Answer 1

yes what is Ford the priblem

Answer 2

To solve the system of equations using elimination, multiply Equation 1 by 4 and Equation 2 by 1. Subtract Equation 4 from Equation 3 to eliminate x. Solve for y and substitute back to solve for x. Each roll of reversible paper costs $16, and each roll of metallic paper costs $9.

Step-by-step explanation:

To write a system of equations to describe the situation, let's assume that the price of each roll of reversible paper is x dollars and the price of each roll of metallic paper is y dollars.

From the given information, we can set up the following equations:

1x + 3y = 43 (Equation 1)

4x + 4y = 100 (Equation 2)

To solve this system of equations using elimination, we can multiply Equation 1 by 4 and Equation 2 by 1:

4x + 12y = 172 (Equation 3)

4x + 4y = 100 (Equation 4)

Subtracting Equation 4 from Equation 3 eliminates the variable x:

12y - 4y = 172 - 100

Simplifying, we get:

8y = 72

Dividing both sides by 8, we find:

y = 9

Now we can substitute the value of y back into either Equation 1 or Equation 2 to solve for x. Let's use Equation 1:

1x + 3(9) = 43

Simplifying, we get:

x + 27 = 43

Subtracting 27 from both sides, we find:

x = 16

Therefore, each roll of reversible paper costs $16, and each roll of metallic paper costs $9.