SOLUTION: Having problem setting up this word problem You wish to make a 34 lb bag of feed worth .42 cents per pound by mixing one kind worth .28 cents per pound and another worth .52 cent

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Question 1053910: Having problem setting up this word problem
You wish to make a 34 lb bag of feed worth .42 cents per pound by mixing one kind worth .28 cents per pound and another worth .52 cents per pound. How many pounds of the cheaper food will you need.
I get 14.28 of the cheaper and 19.72 of the expensive one not sure if this good enough my professor says it's 14 and 20 but does not indicate to round.

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You have two significant figures in each piece of numeric information.

x and y, pounds of cheap and expensive ingredient feed items;

system%28x%2By=34%2C0.28x%2B0.52y=0.42%2A34%29

28x%2B52y=42%2A34
7x%2B13y=21%2A17

y=34-x
substitute into the money or price equation now which has been simplified.
7x%2B13%2834-x%29=21%2A17
7x%2B442-13x=357
-6x=357-442
6x=85
x=86%2F6
highlight%28x=14%261%2F6%29, or decimalized, highlight%28x=14.166666repeating=14.17%29

Look very closely at the given 34 pounds of mixture feed to make. This IS to the nearest whole pound, the nearest 1 pound. Just how finely can the feed ingredients be measured? Are you allowed to the nearest half pound, or nearest quarter pound, or maybe the nearest one-ounce? No indication. You are only given, "make a 34 pound bag of feed". You are not given any assumptions to use; no mention of any accuracy needed other than your two significant figures for all given information. If this is the only way your facts are given, then your answer for the cheap feed, x, should be 14, because the computed 14%261%2F6=14.17 will only be read or measured at best without any assumptions, to 14, because 14.17 is closer to 14 than to 15.

Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
.
I assume that yours 0.42 cents per pound and 0.52 cents per pounds in your condition are mistakes.