SOLUTION: To create a breakfast beverage, grapefruit juice in two concentrations, 13% and 37% are combined together and mixed before being added with another juice. If 270 gallons of the 13%

Question 1107389: To create a breakfast beverage, grapefruit juice in two concentrations, 13% and 37% are combined together and mixed before being added with another juice. If 270 gallons of the 13% juice is used, how many gallons of the 37% juice must be used to obtain a 17% grapefruit juice solution
Found 2 solutions by VFBundy, greenestamps:
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!

Cross-multiply:

0.13*(270) + 0.37x = 0.17(270 + x)

Simplify:

35.1 + 0.37x = 45.9 + 0.17x

0.20x = 10.8

Solve for x:

x = 54
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Here is a complete different method for solving mixture problems like this which, if you understand it, can get you to the answers much faster and with far less effort then the traditional algebraic method.

(1) The percentage of the mixture, 17%, is 1/6 of the way from 13% to 37%, the percentages of the two ingredients. (37-13 = 24; 17-13 = 4; 4/24 = 1/6)
(2) Therefore, 1/6 of the mixture needs to be the 37% juice.

That means 5/6 of the mixture is the 270 gallons of 13% juice, making the ratio of the amounts of the two ingredients 5:1. Then, since 270 gallons of the 13% juice were used, the amount of 37% juice that was used was 270/5 = 54 gallons.
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