SOLUTION: The Royal Fruit Company produces two types of fruit drinks. The first type is 30% pure fruit juice, and the second type is 70% pure fruit juice. The company is attempting to produc

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Question 1201079: The Royal Fruit Company produces two types of fruit drinks. The first type is 30% pure fruit juice, and the second type is 70% pure fruit juice. The company is attempting to produce a fruit drink that contains 60% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 60% pure fruit juice?
Found 3 solutions by mananth, josgarithmetic, greenestamps:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

Juice 1 30% ---------------- x pints
juice 2 70% ---------------- 80 - x pints
Mixture 60.00% ---------------- 80
Juice 1 0.3 ---------------- x pints
juice 2 0.7 ---------------- 80 - x pints
Mixture 0.60 ---------------- 80

0.3 x + 0.7 ( 80 - x ) = 80.00 * 0.60

0.3 x + 56 - 0.7 x = 48.00
0.3 x - 0.7 x = 48 - 56
-0.4 x = -8
/ -0.4
x = 20 pints 30.00% Juice 1
60 pints 70.00% juice 2

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Most of these "Royal Fruit Company" mixture questions are the same or same types, only differing in some of the given values.


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Company produces two types of fruit drinks. The first type is 30% pure fruit juice, and the second type is 70% pure fruit juice.
The company is attempting to produce a fruit drink that contains 60% pure fruit juice.
How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 60% pure fruit juice?
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Company produces two types of fruit drinks. The first type is L% pure fruit juice, and the second type is H% pure fruit juice.
The company is attempting to produce a fruit drink that contains T% pure fruit juice. How many pints of each of the two existing
types of drink must be used to make V pints of a mixture that is T% pure fruit juice?
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If g is how many pints of the H% liquid, then
V-g is how many pints of the L% liquid.

Accounting for amount of the PURE fruit juice: highlight_green%28Hg%2BL%28V-g%29=T%2AV%29.
You can substitute the given values whenever you want, and should hold-off on computations until
the end.

Hg%2BLV-Lg=TV
Hg-Lg=TV-LV
%28H-L%29g=V%28T-L%29
highlight%28g=V%28%28T-L%29%2F%28H-L%29%29%29

..
..

The percentages 30, 60, 70
The quantity to make 80 pints

g=80%28%2860-30%29%2F%2870-30%29%29
g=80%2830%2F40%29
g=80%283%2F4%29
g=60------------pints of the 70% juice

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Tutor @mananth has provided a good standard formal algebraic solution. You can use that as a good example of how the problem can be solved.

Or, if you like to torture yourself, you can also use the rather absurd method tutor @josgarthmetic loves to show on this kind of problem -- with all those variables.

Finally, if a formal algebraic solution is not required, this problem can be solved in a few seconds informally:

The target of 60% is 3/4 of the way from 30% to 70%; therefore, 3/4 of the mixture is the 70% fruit juice.

ANSWER: 3/4 of 80 pints, or 60 pints, is the 70% fruit juice; the other 20 pints is the 30% fruit juice.