Question

Michelle is purchasing fabric for two new sewing projects: a hat and a tote bag. The two projects each need red and black fabric. The hat requires 2 yards of red fabric and 1 yard of black fabric. The tote bag requires 2 yards of red fabric and 4 yards of black fabric. Michelle paid $14 for the hat’s fabric and $26 for the tote bag’s fabric. How much does one yard of each fabric cost?

Answers

  1. The cost of one yard of black fabric is $4.
    The cost of one yard of red fabric is $5.

    What are the linear functions that represent the question?

    2r + b = 14 equation 1
    2r + 4b = 26 equation 2
    Where:
    r = cost of one yard of red fabric
    b = cost of one yard of black fabric

    What is the cost of each type of fabric?

    Subtract equation 1 from equation 2
    3b = 12
    b = 12 / 3
    b = 4
    Substitute for b in equation 1
    2r + 4 = 14
    2r = 14 – 4
    2r = 10
    r = 10 / 2
    r = $5
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