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?

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