|
Question 1182504: The Royal Fruit Company produces two types of fruit drinks. The first type is 45% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 55% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 110 pints of a mixture that is 55% pure fruit juice?
Found 3 solutions by Boreal, greenestamps, josgarithmetic:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x pints of the 45% for 0.45x
110-x pints of the 95% for 104.5-0.95x
that computes the amount of "pure" fruit juice in pints
The final amount is 110 pints of 0.55 fruit juice or 60.5 pints "pure".
So, 0.45x+104.5-0.95x=60.5
-0.50x=-44
x=88 pints of 45% or 39.6 pints "pure"
110-x=22 pints of 95% or 20.9 pints "pure"
Also, 55% is 1/5th of the way between 45 and 95%
so the 45% must be weighted 4/5 and the 95% weighted 1/5 in the final result.
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
A quick and easy non-algebraic method for solving this and any similar two-part mixture problem (if an algebraic solution is not required)....
Think of starting with the 45% fruit juice and adding the 95% fruit juice, stopping when you get to 55%; model that on a number line.
55 is 10/50 = 1/5 of the way from 45 to 95. (55-45=10; 95-45=50)
That means 1/5 of the mixture is the 95% fruit juice you are adding.
ANSWER: 1/5 of 110 pints, or 22 pints, of 95% fruit juice; the other 88 pints of 45% fruit juice.
Answer by josgarithmetic(39623)  (Show Source):
You can put this solution on YOUR website! A large number of mixture questions about The Royal Fruit Company have been answered already on this site.
Low concentration juice, 45%
High concentration juice, 95%
Desired mix concentration, 55%
Quantity of mixture, 110 pints
Quantity of the HIGH CONCENTRATION juice, v
Quantity of low concentration juice, 110-v
 -------to account for amount of pure juice
Solve this for v, and evaluate 110-v.
|
|
|
| |
