chapter 2.2 Q 29 Granny\'s custom quilts receives an order for a quilt made from
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Question
chapter 2.2 Q 29 Granny's custom quilts receives an order for a quilt made from square patches of three types: solid green, solid blue, and floral. the quilt is to be 8 squares by 12 squares, and there must be 15 times as many solid squares as floral squares. if granny's charges $3 per solid square and $5 per floral square and the customer wishes to spend exactly $300 how many of each type of square may be used in the quilt.
I set up the matrix as follows: 15x + 15y + z = 96; 3x + 3y + 5z = 300
Now just looking at the poblem i know the answer is 6 floral squares and 90 of any combination of the solid squares but I have to show the work, set up the matrix enter in my calculator and get the answer. problem is I don't get the correct answer. I even tried x + y +1/15z = 96 ; 3x+3y+5z=300
Explanation / Answer
You are so close, you don't even know it. You are right about the part being 6 florals, and 90 solids. The mistake that you made was that you broke up green and blue solids into two different variables. They never state in the equation that there has to be a set ratio between the blue and green solids, and since they both cost the same, and are the same size (one square) you can treat them as the same variable. You also have to do this, because you only have two equations. The first one telling you how many squares are needed, and the second one telling you how much each square costs. Try running your Matrix again, but this time, instead of saying '15x + 15y' just say '15s' (15 solid) and also, instead of '3x + 3y' also say '3s'. I think that you will find out that this problem works out just like you wanted it. It was worded a little tricky, but now that I have explained it, do you think that you can do the rest of it? (comment back, I read all comments)
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