Question

A quilt maker sews both large and small quilts. A large quilt requires 8 yards of fabric while the small quilt requires 3 yards of fabric. How many of each size quilt did she make if she used a total of 90 yards of fabric to make 15 quilts?

Answer 1

The number of each size quilt is;

`\begin{gathered} \text{ Number of large quilt = 9} \\ \text{ Number of small quilt = }6 \end{gathered}`

Step-by-step explanation:

Given that a large quilt requires 8 yards of fabric while the small quilt requires 3 yards of fabric.

Let x represent the number large quilt and y the number of small quilt.

If she used a total of 90 yards of fabric to make 15 quilts then we have;

`\begin{gathered} 8x+3y=90\text{ ---------1} \\ x+y=15\text{ ----------2} \end{gathered}`

let us solve the system of equations by substitution. From equation 2;

`x=15-y`

substituting into equation 1;

`\begin{gathered} 8x+3y=90 \\ 8(15-y)+3y=90 \\ 120-8y+3y=90 \\ 120-5y=90 \\ 5y=120-90 \\ 5y=30 \\ y=(30)/(5) \\ y=6 \end{gathered}`

substituting the value of y;

`\begin{gathered} x=15-y \\ x=15-6 \\ x=9 \end{gathered}`

Therefore; the number of each size quilt is;

`\begin{gathered} \text{ Number of large quilt = 9} \\ \text{ Number of small quilt = }6 \end{gathered}`