Question 1122997: How much 10% solution and how much 65% solution should be mixed together to make 100 gal of 35% solution?
thank you!
Found 4 solutions by Boreal, josgarithmetic, ikleyn, greenestamps:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x gal of 10% solution
100-x (everything else) of 65% solution
.10x+0.65(100-x)=100*0.35=35
.10x+65-0.65x=35
-.55x=-30
x=54.5 gal of 10% solution
100-x=45.5 gal of 65% solution
Check--their average is 37.5%, a little high, so this should be fairly even between both, skewed towards the 10% solution, which it is.
Answer by josgarithmetic(39617)  (Show Source):
Answer by ikleyn(52786)  (Show Source):
You can put this solution on YOUR website! .
Be aware : The solution by @josgaruthmetic using system of equations I S W R O N G.
A s u s u a l.
For your safety, simply ignore it !
Use the solution by @Boreal instead, which is correct.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Here is a quick way to solve "mixture" problems like this involving two ingredients.
(1) 35% is 5/11 of the way from 10% to 65% (picture the percentages on a number line...):
65-10 = 55; 35-10 = 25; 25/55 = 5/11.
(2) Therefore, 5/11 of the 100 gallons should be the 65% ingredient.
Answer:
10% -- 6/11 of 100 = 600/11 = 54 6/11 gallons
65% -- 5/11 of 100 = 500/11 = 45 5/11 gallons
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