SOLUTION: A beverage manufacturer aims to mix up an 840 gallons batch of a tomato juice blend that contains 26% juice. The manufacturer will be combining a 6% blend and a 31% blend to achiev

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Question 1157584: A beverage manufacturer aims to mix up an 840 gallons batch of a tomato juice blend that contains 26% juice. The manufacturer will be combining a 6% blend and a 31% blend to achieve this. How much of each type should the manufacturer combine to get the desired tomato juice blend?
Found 2 solutions by mananth, josgarithmetic:
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!

A beverage manufacturer aims to mix up an 840 gallons batch of a tomato juice blend that contains 26% juice. The manufacturer will be combining a 6% blend and a 31% blend to achieve this. How much of each type should the manufacturer combine to get the desired tomato juice blend?
Blend A contains 31% juice. let it be x gallons
Blend B contains 6% let it be y gallons
x+y=840------------------1
31%x+6%y = 26%(x+y)
31x+6y=26x+26y
5x-20y=0-----------------2
solve 1 &2
multiply (1) by- 5
-5x-5y=-4200
5x-20y=0
add
-25y = 4200
y=168
168 gallons of blend B
Balance Blend A =840-168=672 gallons

Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
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840 gallons batch of a tomato juice blend that contains 26% juice. The manufacturer will be combining a 6% blend and a 31% blend to achieve this.
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26 is closer to 31 than it is to 6. Most of the blend will be made with the 31% juice.

;

;
---------gallons of the 6% tomato juice

--------gallons of the 31% juice

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More generally, to make M amount of some concentration T percent mixture, starting from H % high concentration and L % low concentration,
let v be the amount of the H% material, and then M-v is amount of the L% material.

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