Mixture A is 15 percent alcohol, and mixture B is 50 percent

Question

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

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I got C. 2.3 can someone confirm?

Sorry to innundate the forum with mixture problems. They have been my weakness. I take too long to figure them out. Its a 500-600 level question. Shouldn't take more than a minute. Just wanted to brush up on it.

MBAhereIcome · Answer

ratio of A to B in the final mixture = 50-30 : 30-15 = 4:3
gallons of A used = 4/7*4 = 2.28

ans: c

LalaB · Answer

one more method-
0.15a+.05b=0.3(a+b)
0.2b=0.15a
20b=15a
b/a=3/4

a=4/7*4=2.3

Ousmane · Answer

Let's the total quantity of A be XA. Then the amount of alcohol is 0.15*XA
Let's the total quantity of A be XB. Then the amount of alcohol is 0.5*XB
From the question we know two things:
1) (0.15*XA + 0.5*XB) / 4 = 3/10 ==> 1.5*XA + 5*XB = 12
2) XA + XB = 4 (or 5*XA + 5*XB = 20)
Then
2) - 1) yields 3.5*XA = 8 ==> X = 80/35 = 16/7 = 2.44.
Since all the answers are getting 2.3 something, my solution may have some logic flaw. Can anyone tell me what's wrong with it?
Many thanks
Brother Karamazov

mbaiseasy · Answer

Fast technique:
1) Get Ratio
2) Calculate gallons using Ratio

(See attached)

Bunuel · Answer

You can treat this question as wighted average problem: weighted \ average=\frac{weight_1*value_1+weight_2*value_2}{value_1+value_2} --> 0.3=\frac{0.15*A+0.5(4-A)}{4} --> A\approx{2.3} . Answer: C. Also you can notice that as wighted average (alcohol share) of final mixture (30%) is closer to that of mixture A (15%) than to that of mixture B (50%) then there should be more of mixture A in final solution of 4 gallons than of mixture B, so answer choices A and B are out right away. Plus, if in final mixture there were equal amounts of mixtures A and B then the final solution would have (15%+50%)/2=32.5% of alcohol, and as 32.5% is a little more than 30% (actual concentration) then there should be a little more of mixture A than mixture B in 4 gallons, answer choice C fits best. OPEN DISCUSSION OF THIS QUESTION IS HERE: mixture-a-is-15-percent-alcohol-and-mixture-b-is-50-percent-107787.html

Mixture A is 15 percent alcohol, and mixture B is 50 percent

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