SOLUTION: To be considered “nectar” a drink must contain 50% fruit juice. Find how much pure (100%) fruit juice and how much fruit drink (30%) must be mixed to make 7 gallons of “necta

Question 1149985: To be considered “nectar” a drink must contain 50% fruit juice. Find how much pure (100%) fruit juice and how much fruit drink (30%) must be mixed to make 7 gallons of “nectar”.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39613) (Show Source): You can put this solution on YOUR website!
x of 30%
y of 100%

You want the value of x.
Answer by greenestamps(13195) (Show Source): You can put this solution on YOUR website!

First, a standard algebraic approach....

You are mixing x gallons of 100% juice and (7-x) gallons of 30% juice to get 7 gallons of 50% juice:

Solve using basic algebra.

Next, a completely different approach which is much faster and easier -- if you understand it....

(1) 50% is 2/7 of the way from 30% to 100% (picture the 3 percentages on a number line, if it helps....)
(2) Therefore, 2/7 of the mixture needs to be what you are adding.

ANSWER: The mixture needs to be 2/7 of the total 7 gallons, or 2 gallons, of the 100% juice, with the other 5 gallons the 30% juice.

RELATED QUESTIONS
The Royal Fruit Company produces two types of fruit drinks. The first type is 40%... (answered by josgarithmetic)
Fruit drink A consists of 6% pure fruit juice and drink B consists of 15% pure fruit... (answered by richwmiller)
Fruit drink A consists of 6% pure fruit juice and drink B consists of 15% pure fruit... (answered by mananth)
Fruit drink A consists of 6% pure fruit juice and drink B consists of 15% pure fruit... (answered by ewatrrr)
The Royal Fruit Company produces two types of fruit drinks. The first type is 80% pure... (answered by josgarithmetic)
The Royal Fruit Company produces two types of fruit drinks. The first type is 80% pure... (answered by ankor@dixie-net.com)
The Royal Fruit Company produces two types of fruit drinks. The first type is 80% pure... (answered by mananth,greenestamps)
The first type is 65% pure fruit juice, and the second type is 90% pure fruit... (answered by addingup)
The Royal Fruit Company produces two types of fruit drinks. The first type is 50% pure... (answered by josmiceli)