Question

Carl is sewing a quilt. The number of yards of green fabric in the quilt is proportional to the number of yards of bluefabric in the quilt. This equation represents the proportional relationship between the number of yards of greenfabric, g, and yards of blue fabric, b, in the quilt.6 2/3 b = 5 1/3 gEnter the number of yards of green fabric used for 1 yard of blue fabric

Answer 1

1 1/4 yards of green fabric.

Explanation:

The equation representing the proportional relationship between the number of yards of green fabric, g, and yards of blue fabric, b, in the quilt is:

`6(2)/(3)b=5(1)/(3)g`

If 1 yard of blue fabric is used: b=1

`\begin{gathered} 6(2)/(3)*1=5(1)/(3)g \\ (20)/(3)=(16)/(3)g \\ \text{ Multiply both sides by }(3)/(16) \\ (3)/(16)*(20)/(3)=(16)/(3)*(3)/(16)g \\ g=(20)/(16) \\ g=1(1)/(4)\text{ yards} \end{gathered}`

If 1 yard of blue fabric is used, then 1 1/4 yards of green fabric will be used.