Question

On Monday, Shelbie bought x yards of blue fabric at Fabulous Fabrics for $3.00 per yard plus a spool of yarn for $2.25. On Tuesday, she bought x yards of blue fabric at Gorgeous Garments for $2.50 per yard plus a pattern for $8.00. Then, on Wednesday, Shelbie bought x yards of blue fabric and some fabric glue at Marvelous Materials. Let f(x) represent the amount Shelbie spent at Fabulous Fabrics, let g(x) represent the amount she spent at Gorgeous Garments, and let m(x) represent the amount she spent at Marvelous Materials. If the blue fabric at Marvelous Materials is 1.2 times the price per yard of blue fabric at Gorgeous Garments, and the fabric glue cost $4.00, complete the equation for the function m(x) below. Then, Shelbie bought 5 more yards of blue fabric at Lovely Linens than she bought at Fabulous Fabrics, and each yard of fabric cost half as much as each yard at Marvelous Materials. If l(x) represents the amount Shelbie spent at Lovely Linens, complete the equation for the function l(x) below.

Answer 1

The equation for the function m(x) is m(x) = $3.00x + $4.00

The equation for the function l(x) is l(x) = $1.50(x + 5)

How to complete the equations for the functions m(x) and l(x)

To complete the equations for the functions m(x) and l(x), break down the given information and solve step by step:

For the function m(x):

Shelbie bought x yards of blue fabric at Marvelous Materials.

The blue fabric at Marvelous Materials is 1.2 times the price per yard of blue fabric at Gorgeous Garments.

The fabric glue cost $4.00.

The cost of the blue fabric at Marvelous Materials per yard is 1.2 times the price at Gorgeous Garments, which is $2.50.

So, the cost of the blue fabric at Marvelous Materials per yard is 1.2 * $2.50 = $3.00.

The cost of x yards of blue fabric at Marvelous Materials is then $3.00 * x.

Adding the cost of the fabric glue, the equation for the function m(x) becomes:

m(x) = $3.00x + $4.00

For the function l(x):

Shelbie bought 5 more yards of blue fabric at Lovely Linens than she bought at Fabulous Fabrics.

Each yard of fabric at Lovely Linens cost half as much as each yard at Marvelous Materials.

Let's assume Shelbie bought y yards of blue fabric at Fabulous Fabrics.

The cost per yard of fabric at Lovely Linens is half the cost at Marvelous Materials, which is $3.00 / 2 = $1.50.

The cost of y + 5 yards of blue fabric at Lovely Linens is then $1.50 * (x + 5).

The equation for the function l(x) becomes:

l(x) = $1.50(x + 5)