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.

Let 'x' represent the number of yards of silk and 'y' represent the number of yards of cotton.
Here is a system of equations that represent the constraints in the situation.
x+y=4.25
16.90x+4y=36.35
Find the solution to the system of equations. You may use any method you want, but you must explain your reasoning and methods fully.

Answer 1

Explanation:

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

The two equations are known as simultaneous equation. They would be solved using 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

Answer 2

Explanation:

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

The two equations are known as simultaneous equation. They would be solved using 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