Question

X + y = 4.25

16.90x + 4y = 36.35
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.
Here is a system of equations that represent the
constraints in the situation.
What does the solution to the system represent?

Find the solution to the system of equations.

Answer 1

The yards of silk bought is equal to 1.49 yards and the yard of cotton bought is equal to 2.76 yards.

Explanation:

The two equations would be solved using the elimination method.

x + y = 4.25 equation 1

16.90x + 4y = 36.25 equation 2

where:

x = yards of silk bought

y = yards of cotton bought

In order to determine the value of x, multiply equation 1 by 4.

4x + 4y = 17 equation 3

Subtract equation 3 from 2

19.25 = 12.90x

Divide both sides of the equation by 12.90

x = 1.49 yards

In order to determine the value of y, substitute for x in equation 1

1.49 + y = 4.25

y = 4.25 - 1.49

y = 2.76 yards