SOLUTION: Can you help me solve this problem/ How much of a 60% orange juice drink must be mixed with 14 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: Can you help me solve this problem/ How much of a 60% orange juice drink must be mixed with 14 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1153682: Can you help me solve this problem/
How much of a 60% orange juice drink must be mixed with 14 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice
The amount of 60% orange juice drink is ____ gallons
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
---------------------------------------------------------------
How much of a 60% orange juice drink must be mixed with 14 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice?
--------------------------------------------------------------

v gallons of 60%

60v%2B20%2A14=50%28v%2B14%29----------solve for v.
-
60v%2B20%2A14=50v%2B50%2A14
60v-50v=50%2A14-20%2A14
v%2860-50%29=14%2850-20%29
v=14%28%2850-20%29%2F%2860-50%29%29
v=14%2A3
highlight%28v=42%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 method that will get you to the answer to this and many similar problems with very little effort.

Think of the problem as starting with 20% juice and adding 60% juice, stopping when the mixture is 50% juice.

50% is 3/4 of the way from 20% to 60%. (20 to 60 is 40; 20 to 50 is 30; 30/40 = 3/4.)

That means 3/4 of the mixture must be the 60% juice you are adding.

So the original 14 gallons of 20% juice is 1/4 of the mixture; that means the 3/4 of the mixture that is the added 60% juice is 3*14 = 42 gallons.