To determine the amount Shelbie spent at Marvelous Materials, we define [tex]\( m(x) \)[/tex] as follows:
1. The price per yard at Marvelous Materials is 1.2 times the price per yard at Gorgeous Garments.
2. Given that the price per yard at Gorgeous Garments is \[tex]$2.50, the price per yard at Marvelous Materials is \( 1.2 \times 2.50 = 3.00 \) dollars per yard.
3. The additional cost for fabric glue is \$[/tex]4.00.
Thus, the total amount spent at Marvelous Materials, [tex]\( m(x) \)[/tex], can be described by the linear function:
[tex]\[
m(x) = 3.00x + 4.00
\][/tex]
Next, to determine the amount Shelbie spent at Lovely Linens, we define [tex]\( l(x) \)[/tex] as follows:
1. At Lovely Linens, Shelbie bought 5 more yards of fabric than at Fabulous Fabrics. Hence, the total yards bought at Lovely Linens is [tex]\(x + 5\)[/tex].
2. The price per yard at Lovely Linens is half the price per yard at Marvelous Materials. Thus, [tex]\( \frac{1}{2} \times 3.00 = 1.50 \)[/tex] dollars per yard.
The total amount spent at Lovely Linens, [tex]\( l(x) \)[/tex], can then be described by the linear function:
[tex]\[
l(x) = 1.50(x + 5) = 1.50x + 7.50
\][/tex]
To summarize, the completed equations are:
[tex]\[
m(x) = 3.00x + 4.00
\][/tex]
[tex]\[
l(x) = 1.50x + 7.50
\][/tex]
