SOLUTION: Linda needs 10 gallons of solution that is 60% antifreeze. She has a solution that is 90% antifreeze and another that is 50% antifreeze. How much of each should she use?

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Linda needs 10 gallons of solution that is 60% antifreeze. She has a solution that is 90% antifreeze and another that is 50% antifreeze. How much of each should she use?      Log On

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Question 1180731: Linda needs 10 gallons of solution that is 60% antifreeze. She has a solution
that is 90% antifreeze and another that is 50% antifreeze. How much of each
should she use?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
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Linda needs 10 gallons of solution that is 60% antifreeze. She has a solution
that is 90% antifreeze and another that is 50% antifreeze. How much of each
should she use?
--------------------------------------------------------------

If v gallons of the 90% then 10-v gallons of the 50%

pure antifreeze account!
90v%2B50%2810-v%29=60%2A10

9v%2B5%2810-v%29=60
9v%2B50-5v=60
4v=10
highlight%28v=5%2F2=2%261%2F2%29gallons for the 90%
-
highlight%287%261%2F2%29gallons for the 50%







For ANY such general two-part mixture percents problem
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Linda needs M gallons of solution that is T% antifreeze. She has a solution
that is H% antifreeze and another that is L% antifreeze. How much of each
should she use?
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v for the H% material
M-v for the L% material

highlight_green%28Hv%2BL%28M-v%29=TM%29

Hv%2BLM-Lv=TM
Hv-Lv=TM-LM
%28H-L%29v=M%28T-L%29
highlight%28v=M%28%28T-L%29%2F%28H-L%29%29%29

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


If a formal algebraic solution is not required, here is a fast and easy path to solving any two-part mixture problem like this.

(1) The target 60% is 10/40=1/4 of the way from 50% to 90%. (Picture the three percentages 50, 60, and 90 on a number line, if it helps. 60 is 10/40 = 1/4 of the way from 50 to 90.)
(2) That means 1/4 of the 10-gallon mixture should be the 90% antifreeze.

ANSWER: 1/4 of 10 gallons, of 2.5 gallons, of the 90% antifreeze, and the other 7.5 gallons of 50% antifreeze.

CHECK:
.50(7.5)+.90(2.5)=3.75+2.25=6
.60(10)=6