How many liters of a 14% alcohol solution must be mixed with 20 liters of a 50% solution to obtain a 30% solution?

Question

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Answer 1

If 30% was the simple average of 50% and 14% (which it is not) then equal amount of 50% and 14% are used.

 

So here we think to estimate first. It is always a good strategy to start with. Since 50+14 = 64 AND 64/2 =32, 

 

but our solution is lower , 30% it means that  more of the 14% solution is used compared to the 50% solution.

 

So our answer should be more than 20 liters!! but not much more because our 32 avg is pretty close to 30

 

 

 

.14X + .5(20) = .30(X+20)  distribute     The 2 PARTS EQUAL THE WHOLE FOR AMOUNT OF ALCOHOL

 

.14X + .5(20) = .30X + 6  subtract .14x from both sides and multiply .5 x 20

 

10 = .16X + 6   subtract 6 from both sides

 

4 = .16X   Divide both sides by .16

 

25 = X