SOLUTION: 15 pounds of nuts are available for baking. One pound of nuts makes 32 brownies. 1.5 pounds of nuts makes 24 pieces of fudge. I want twice as many pieces of fudge as brownies.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 15 pounds of nuts are available for baking. One pound of nuts makes 32 brownies. 1.5 pounds of nuts makes 24 pieces of fudge. I want twice as many pieces of fudge as brownies.       Log On


   

Question 992697: 15 pounds of nuts are available for baking. One pound of nuts makes 32 brownies. 1.5 pounds of nuts makes 24 pieces of fudge. I want twice as many pieces of fudge as brownies. How much of each should make?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
b, how many brownies
f, how many fudges
f%2Fb=2
f=2b
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15 pounds of nuts; no specific quantity of fudges or brownies was asked for, just a ratio given, so we might expect we want to use ALL 15 pounds of the nuts.

Accounting for the given pounds of nuts:
b%2A%281%2F32%29%2Bf%2A%281.5%2F24%29=15
and a relationship between f and b was already established and ready for the substitution.
%281%2F32%29b%2B%281.5%2F24%29%2A2b=15
b%281%2F32%2B3%2F24%29=15
b%28%281%2F32%29%2B%281%2F8%29%29=15
b%281%2F32%2B4%2F32%29=15
b%285%2F32%29=15
b=15%2832%2F5%29
highlight%28b=96%29-------this many brownies can be made.

f=2%2Ab
f=2%2896%29
highlight%28f=192%29--------this many bars of fudge can be included.

Trick was to decide what variables to assign, but this can come from carefully analyzing the problem description and the question.