Question

A craft store is having a clearance sale where ribbon and fabric are sold at a discounted prices per yard. Gwen and Penelope both made purchases during the clearance. Gwen bought 6 yards of ribbon and 10 yards of fabric for a total of $66.50. Penelope bought 5 yards of ribbon and 8 yards of fabric for a total of $53.50. What is the discounted price per yard for ribbon and for fabric?

A. Ribbon costs $1.50 per yard, and fabric costs $5.75 per yard.
B. Ribbon costs $2.15 per yard, and fabric costs $7.50 per yard.
C. Ribbon costs $5.75 per yard, and fabric costs $1.50 per yard.
D. Ribbon costs $7.50 per yard, and fabric costs $2.15 per yard.

Answer 1

The discounted price per yard for ribbon is $1.50 and for fabric is $5.75.

Step-by-step explanation:

To find the discounted price per yard for ribbon and fabric, we can set up a system of equations using the given information:

Let r be the price per yard of ribbon.
Let f be the price per yard of fabric.

We have the following equations:

6r + 10f = 66.50 (equation 1)
5r + 8f = 53.50 (equation 2)

We can solve this system of equations to find the values of r and f. Multiplying equation 1 by 5 and equation 2 by 6 gives us:

30r + 50f = 332.50 (equation 3)
30r + 48f = 321.00 (equation 4)

Subtracting equation 4 from equation 3 eliminates r:

2f = 11.50

Divide both sides by 2:

f = 5.75

Substituting the value of f back into equation 2 gives us:

5r + 8(5.75) = 53.50

5r + 46 = 53.50

5r = 7.50

Divide both sides by 5:

r = 1.50

Therefore, the discounted price per yard for ribbon is $1.50 and for fabric is $5.75.