Problem Solving

BTGmoderatorLU wrote:Source: Princeton Review

Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?

A. 1.5
B. 1.7
C. 2.3
D. 2.5
E. 3.0

The OA is C

Say mixture A is x gallons and mixture B is y gallons.

Thus, total amount of alcohol in the combined mixture = 15% of x + 50% of y = 0.15x + 0.5y

Again, the amount of alcohol in the combined mixture = 30% of 4 = 1.2 gallons

Thus, 0.15x + 0.5y = 1.2

We also know that x + y = 4. Tus, y = 4 - x

Plugging-in the value of y = 4 - x in 0.15x + 0.5y = 1.2, we get x = ~2.3

The correct answer: C

Hope this helps!

-Jay
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Hi All,

We're told that Mixture A is 15 percent alcohol and mixture B is 50 percent alcohol and when a certain amount of each is poured together to create a 4-gallon mixture, the result contains 30 percent alcohol. We're asked approximately how many gallons of mixture A are in the mixture. This "mixture" question can be approached in a number of different ways, including by TESTing THE ANSWERS.

To start, IF we had an EQUAL amount of each Mixture, then the average of the 4-gallon mixture would be (15 + 50)/2 = 65/2 = 32.5% alcohol. This result is TOO HIGH though; the actual mixture is 30%. This means that we'll need a little more of Mixture A... meaning that a little more than 2 gallons (of the 4-gallon total) will be Mixture A. Looking at the answer choices, it's highly likely that the correct answer is Answer C.

We can actually check to see if either Answer C is a match or if Answer D is "too small." We're looking for an answer that would lead to (4)(.3) = 1.2 gallons of alcohol. Answer D is a little 'easier' to work with, so let's TEST that Answer....

Answer D: 2.5 gallons

IF.... we have 2.5 gallons of Mixture A, then we have 4 - 2.5 = 1.5 gallons of Mixture B...
(2.5)(.15) + (1.5)(.5) =
.375 + .75 =
1.125 gallons of Alcohol. This answer is TOO SMALL (we need there to be 1.2 gallons of alcohol). To get more alcohol we need LESS of Mixture A than we have here. There's only one answer that fits...

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorLU wrote:Source: Princeton Review

Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?

A. 1.5
B. 1.7
C. 2.3
D. 2.5
E. 3.0

We let a = the number of gallons of mixture A and b = the number of gallons of mixture B. We can create the equations:

a + b = 4

b = 4 - a

and

0.15a + 0.5b = 0.3(a + b)

15a + 50b = 30a + 30b

20b = 15a

4b = 3a

Substituting we have:

4(4 - a) = 3a

16 - 4a = 3a

16 = 7a

a = 16/7 ≈ 2.3

Answer: C