One gallon of soft drink is made of 40% orange juice and 60%

AAPL wrote:One gallon of soft drink is made of 40% orange juice and 60% water, how many additional gallons of orange juice must be mixed in to make the orange juice 60% of the soft drink?

A. 0.5
B. 1
C. 1.25
D. 1.5
E. 2

IMPORTANT CONCEPT: when we combine EQUAL amounts of two mixtures, the concentration of the resulting mixture will be the AVERAGE of the two mixtures.
For example, if we combine 1 liter of a 10% salt solution with 1 liter of a 40% salt solution, the RESULTING solution will be 25% salt, since (10+40)/2 = 25.

So, If we take 1 gallon of soft drink with 40% orange juice and add an EQUAL amount (1 gallon) of 100% orange juice, then the resulting mixture will be 70% orange juice.
We want the resulting mixture to be 60% orange juice. So, we need to add LESS THAN 1 gallon of 100% orange juice

Check the answer choices . . . only one option (A) is less than 1 gallon.

Answer: A

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AAPL wrote:One gallon of soft drink is made of 40% orange juice and 60% water, how many additional gallons of orange juice must be mixed in to make the orange juice 60% of the soft drink?

A. 0.5
B. 1
C. 1.25
D. 1.5
E. 2

We are given that one gallon of soft drink contains 0.4 gallons of OJ and 0.6 gallons of water. To make OJ 60%, we can let n = the number of gallons of additional OJ and create the following equation:

(0.4 + n)/(1 + n) = 0.6

0.4 + n = 0.6 + 0.6n

0.4n = 0.2

n = 1/2

Alternate Solution:

We start with 1 gallon of 40% orange juice. To it we add g gallons of 100% orange juice, yielding (1 + g) gallons of 60% orange juice. We can express this in an equation as:

1 x 0.40 + g x 1.0 = (1 + g) x 0.60

0.4 + g = 0.6 + 0.6g

0.4g = 0.2

4g = 2

g = 1/2

Answer: A