SOLUTION: A concrete mixture is to be made which contains 35% sand by weight and 642 lb of mixture containing 29% sand is already on hand. How many pounds of sand must be added to this mixt

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Question 730607: A concrete mixture is to be made which contains 35% sand by weight and 642 lb of mixture containing 29% sand is already on hand. How many pounds of sand must be added to this mixture to arrive at the required 35%?
I tried .29(642 + x)= .35x
.29(642) = .35 (642 + x)
I'm having trouble asking myself the right questions to set the problem up correctly...please help Mark
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Letting x = pounds of sand to add to reach 35% sand,

highlight%28%28642%2A0.29%2Bx%29%2F%28642%2Bx%29=0.35%29, the fundamental ratio for the adjustment, and as you wanted, using decimal fractions instead of "percents" units.
642%2A0.29%2Bx=0.35%28642%2Bx%29
642%2A0.29%2Bx=0.35%2A642%2B0.35x
.
642%280.29-0.35%29=%280.35-1%29x
642%280.35-0.29%29=%281-0.35%29x
.
x=%280.06%2F0.65%29642
highlight%28x=59%29


SOME COMMENTS:
The numerator in the ratio equation is the total sand present in the adjusted mixture. The denominator in the ratio equation is the total amount of adjusted mixture. The entire ratio, the left-hand member of the equation, must be equal to the specified 0.35, or 35%.
Since the percents given in the description only go to two significant figures, I kept my result answer to two significant figures also. If we could allow for THREE significant figures, our answer should probably be more like 59.3 pounds of sand.