SOLUTION: Brenda plans to make blue and purple scarfs in 2 two sizes: medium and large. She has a total of 60 yards of fabric for each color. She will need 1/4 of a yard for medium scarves a

Question 408437: Brenda plans to make blue and purple scarfs in 2 two sizes: medium and large. She has a total of 60 yards of fabric for each color. She will need 1/4 of a yard for medium scarves and will need 1/2 a yard for large scarves. She also wants to add ribbon as a trimming to her scarves. She has a total of 240 yards of ribbon in each color. For the medium scarves, she will need 1 yard of ribbon and for the large, 2 yards. Set up two equations to solve for the number of scarves per color that can be made.
I am unsure of the equation to use.
Thus far, I have:
m=medium scarves and l=large scarves
1/4x+1/2y=60
1x+2y=240
This does not look like the appropriate form. Am I on the right track?

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Brenda plans to make blue and purple scarfs in 2 two sizes: medium and large.
She has a total of 60 yards of fabric for each color.
She will need 1/4 of a yard for medium scarves and will need 1/2 a yard for large scarves.
She also wants to add ribbon as a trimming to her scarves.
She has a total of 240 yards of ribbon in each color.
For the medium scarves, she will need 1 yard of ribbon and for the large, 2 yards.
Set up two equations to solve for the number of scarves per color that can be made.
:
I think you have the right idea here.
Developing what you already have: x = med scarves, y = lg scarves
.25x + .5y = 60; fabric eq:
and
1x + 2y = 240; ribbon eq:
:
If you multiply the 1st equation by 4, both equations are the same, there is no unique solution
:
There are many solutions, we can find the number of each size like this:
x = 240-2y
For example if you have 50 lg scarves, y = 50
x = 240-2(50)
x = 240 - 100
x = 140 med scarves
or
If you have 80 lg scarves, y = 80
x = 240-2(80)
x = 240 - 160
x = 80 med scarves
:
:
You can see that both these x,y values will satisfy your original equations.

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