Question

3. At a fabric store, fabrics are sold by the yard. A dressmaker spent $36.35 on4.25 yards of silk and cotton fabrics for a dress. Silk is $16.90 per yard and cottonis $4 per yard. Here is a system of equations that represent the constraints in thesituation.2+ y = 4.2516.90. + 4y = 36.353a. What does the solution to the system represent?Your answer3b. Find the solution to the system of equations. Explain or show yourreasoning.

Answer 1

Given,

The equations are,

$\begin{gathered} x+y=4.25 \\ 16.90x+4y=36.35 \end{gathered}$

a)The solution of the system represents the number of yards of silk and cotton febric purchased by the dressmakers.

Here, x is the number of yards of silk febric.

y is the number of yards of cotton febric.

b) Taking the first equation as,

$x=4.25-y$

Substituting the value of x in equation second then,

$\begin{gathered} 16.90(4.25-y)+4y=36.35 \\ 71.825-16.90y+4y=36.35 \\ -12.90y=-35.475 \\ y=2.75\text{ yards} \end{gathered}$

Substituting the value of y in equation first then,

$\begin{gathered} x=4.25-2.75 \\ x=1.5\text{ yards} \end{gathered}$

The solution of the system is x = 1.5 and y = 2.75 .

Hence, the number of yards silk and cotton febric purchased by dressmaker is 1.5 yards and 2.75 yards respectively.