To make a quilt, a quilter is buying fabric in two colors, blue and green. The quilter needs at least 9.5 yards of fabric in total.
The blue fabric costs $9 a yard.
The green fabric costs $13 a yard.
The quilter can spend up to $110 on fabric.
Let x represent the number of blue yards of fabric purchased and let y represent the number of green yards of fabric purchased.

Please solve the Inequalities.

3.375 yards of blue fabric and 6.125 yards of green fabric was purchased.

Let x represent the number of blue yards of fabric purchased and let y represent the number of green yards of fabric purchased.

Hence:

x + y ≥ 9.5   (1)

The quilter can spend up to $110 on fabric. Hence:

9x + 13y ≤ 110    (2)

The solution to the inequality is:

x = 3.375, y = 6.125

3.375 yards of blue fabric and 6.125 yards of green fabric was purchased.

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Step-by-step explanation:

step one:

given data

blue fabric costs $9 a yard.

green fabric costs $13 a yard.

Let x represent the number of blue yards of fabric purchased and

let y represent the number of green yards of fabric purchased.

Step two:

The quilter needs at least 9.5 yards of fabric in total.

x+y>=9.51

The quilter can spend up to $110 on fabric.

9x+13y<=1102

from equation

x+y>=9.5

x=9.5-y

put x=9.5-y in equation 2 we have

9(9.5-y)+13y<=1102

85.5-9y+13y=110

4y=110-85.5

4y=24.5

y=24.5/4

y=6.125

put y=6.125 in x=9.5-y to find x

x=9.5-6.125

x=3.375

Hence the quilt can purchase

3.375yards of  blue fabric

6.125yards of  green fabric