A quilt maker plans on making 14 quilts using 113 yards of fabric

Question

A quilt maker plans to make 14 quilts this year from 113 yards of fabric. A small quilt requires 4 yards of fabric. A medium quilt requires 7 yards of fabric and a large quilt requires 11 yards of fabric. She plans to make twice as manny large quilts as small quilts.how many of each type of quilt should she make?

Answer 1

Is the wording complete?

 

On the one hand, she could make 6 large ones (11 yds each) and 3 small ones (half as many small as large, as her 'plans' are, at 4 yds each for the small ones) and 5 medium ones (at 7 yds each) and will use up exactly her 113 yards:

 

6*11 yards + 3*4 yards + 5 * 7 yards = 113 yards exactly to make 6 large, 5 medium, and 3 small. I can show you how to get this solution, but, the problem seems to lack some detail:

 

It does not say one has (or that she wants to) use up all her fabric.

 

For example, she could make no large ones, no small ones (thus still meet the goal of "twice as many large as small" since both are zero) and make 16 medium sized ones, using up 16*7 which would take 112 out of the 113 yards.

 

Are "6 large, 5 medium, and 3 small" actually 'better' than "16 medium ones"?

 

The wording of the problem does not give us a requirement or a specific reason to prefer the former to the latter, for example.

 

It might be a poorly worded problem on purpose or due to author carelessness, if you copied the entire complete wording of the problem correctly. Or perhaps there are explicitly or implicitly, additional requirements in the material this is from.