SOLUTION: One canned juice drink is 30% orange juice; another is 5% orange juice. How many liters of each should be mixed together in order to get 25 L that is 9% orange juice?
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Question 1205792: One canned juice drink is 30% orange juice; another is 5% orange juice. How many liters of each should be mixed together in order to get 25 L that is 9% orange juice?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
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One canned juice drink is 30% orange juice; another is 5% orange juice. How many liters of each should be mixed together in order to get 25 L that is 9% orange juice?
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Every two-part mixture of this type works the SAME way.
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One canned juice drink is H% orange juice; another is L% orange juice. How many liters of each should be mixed together in order to get M liters that is T% orange juice?
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v, the volume of the H% orange juice drink
M-v, the volume of the L% orange juice drink
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Substitute what you are given, and evaluate.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
Oh, dear ...!
There is that tutor who loves that monstrous magical formula with a multitude of variables for solving mixture problems like this....
If you are a fan of "doing" mathematics by plugging numbers into formulas without having any understanding of what you are doing, go ahead and solve the problem that way.
If you want to UNDERSTAND what you are doing to solve the problem, there are better ways.
The standard algebraic solution method is to write and solve an equation that says the amount of orange juice in the mixture is the sum of the amounts in the two ingredients. For this problem, that equation says that 30% of the first ingredient plus 5% of the second yields 25L of mixture that is 9% orange juice.
Letting x be the number of gallons of 30% orange juice means the number of gallons of 5% orange juice is 25-x. Then the equation is
I leave it to the student to finish the solution by that method. It involves basic algebra, although the decimals complicate things a bit.
And here is an informal method for solving any two-part mixture problem like this.
For this problem, we are mixing 30% orange juice with 5% orange juice to get 9% orange juice.
Observe/calculate that 9% is 4/25 of the way from 5% to 30%. (Use the numbers 5, 9, and 30 on a number line if it helps.)
That means 4/25 of the mixture is the 30% orange juice.
4/25 of 25L is 4L.
ANSWER: You need 4L of the 30% orange juice and 25-4 = 21L of the 5% orange juice
CHECK:
.30(4)+.05(21) = 1.20+1.05 = 2.25
.09(25) = 2.25
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