Question

At a fabric store, fabrics are sold by the yard. A dressmaker spent $36.35 on 4.25 yards of silk and cotton fabrics for a dress. Silk is $16.90 per yard and cotton is $4 per yard.
Find the solution of the system of equations. Explain or show your reasoning
{x+y=4.25} ; {16.90x+4y=36.35}

Answer 1

Answer:

The number of yards of silk = x = 1.5 yards

The number of yards of cotton = y = 2.75yards

Step-by-step explanation:

At a fabric store, fabrics are sold by the yard. A dressmaker spent $36.35 on 4.25 yards of silk and cotton fabrics for a dress. Silk is $16.90 per yard and cotton is $4 per yard.

Find the solution of the system of equations. Explain or show your reasoning

{x+y=4.25} ; {16.90x+4y=36.35}

Let the number of yards of silk = x

The number of yards of cotton = y

We are given the system of equations:

{x+y=4.25} ......Equation 1

x = 4.25 - y

{16.90x+4y=36.35}....... Equation 2

4.25 - y for x in Equation 2

16.90(4.25 - y) + 4y = 36.35

71.825 - 16.90y + 4y = 36.35

71.825 - 36.35 = 16.90 - 4y

35.475 = 12.90y

y = 35.475/12.90

y = 2.75 yards.

The number of yards of cotton = y

{x+y=4.25} ......Equation 1

x = 4.25 - y

x = 4.25 - 2.75

x = 1.5 yards

The number of yards of silk = x = 1.5 yards