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how many pounds of meal

The manager of a farmer's market has 450 lb of grain that costs $1.60 per pound. How many pounds of meal costing $0.80 per pound should be mixed with the 450 lb of grain to produce a mixture that costs $1.40 per pound?

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Kristen F. | Pre-Algebra, Algebra, Trigonometry, Probability, Statistics, CalcPre-Algebra, Algebra, Trigonometry, Prob...
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Since we wish the mixture to cost 1.40 per pound be part grain (x) and part meal (1-x) we see that
1.40=1.6*x+.8*(1-x)
1.40=.8+.8x
.6=.8x
x=.75. So then 75% of the mixture is grain and 25% is meal. Since there is 1/3 as much meal as there is grain (25%/75%=1/3) we need 450/3=150lbs of meal.