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. Here is a system of equations that represent the constraints in the situation. x + y = 4.25 16.90x + 4y = 36.35 Find the solutions to the system of equations. Explain or show your reasoning

Answer 1

Given:

The system of equations that represent the constraints for the given situation is

$x+y=4.25$

$16.90x+4y=36.35$

To find:

The solution of given system of equations.

Solution:

We have,

$x+y=4.25$           ...(i)

$16.90x+4y=36.35$           ...(ii)

Multiply equation (i) by 4.

$4x+4y=17$           ...(iii)

Subtracting (iii) from (ii), we get

$16.90x+4y-(4x+4y)=36.35-17$

$16.90x+4y-4x-4y=19.35$

$12.90x=19.35$

Divide both sides by 12.90.

$x=\dfrac{19.35}{12.90}$

$x=1.5$

Put this value in (i).

$1.5+y=4.25$

$y=4.25-1.5$

$y=2.75$

The solution of system of equations is x=1.5 and y=2.75. It means, the yards of silk are 1.5 and yards of cotton are 2.75.