A certain solution that is 30 percent acid is obtained by mixing x

Question

A certain solution that is 30 percent acid is obtained by mixing x gallons of a 20 percent acid solution with y gallons of a 60 percent acid solution, where the percents are according to volume. How many gallons of the 60 percent acid solution must be used to obtain 10 gallons of the 30 percent acid solution?
A. 0.75
B. 2.5
C. 3.3
D. 4.0
E. 5.0

A. 0.75
B. 2.5
C. 3.3
D. 4.0
E. 5.0

kayze · Accepted Answer

Here is what I did using equations:

The amount of acid in the final mixture would be 3 gallons, since it is 10 gallons total and 30% of it is acid.

Since 20% of x is acid and 60% of y is acid, then we can find the total amount of acid in a mixture of the two via the formula: 0.2x + 0.6y

Thus, we have 0.2x + 0.6y = 3

Since we know the total mixture volume is 10 gallons, we know x + y = 10 and x = 10 - y. Therefore, we have 0.2(10 - y) + 0.6y = 3
2 - 0.2y + 0.6y = 3
2 + 0.4y = 3
0.4y = 1
y = 1/0.4 = 1/(4/10) = 10/4 =  2.5 gallons

rfrederick1211 · Answer

A certain solution that is 30 percent acid is obtained by mixing x gallons of a 20 percent acid solution with y gallons of a 60 percent acid solution, where the percents are according to volume. How many gallons of the 60 percent acid solution must be used to obtain 10 gallons of the 30 percent acid solution?
A. 0.75
B. 2.5
C. 3.3
D. 4.0
E. 5.0

A. 0.75
B. 2.5
C. 3.3
D. 4.0
E. 5.0

Here's the teeter-totter method: If you have 2 percentages of the additive solution and the final solution percentage, you set up up a line with with the two additive solutions with the final solution in the middle 20-----30------60, you find the difference to the final solution, 10 and 30, then reduce, 1:3, whichever is closest to the final solution (20) you give that the favor of the larger amount, so its 1:3 (1/4) 60 solution and 3:1(3/4) 20 solution, multiply 1/4 by 10 gallons to find the answer. 2.5

Hope that helps

gmatophobia · Answer

Volume of the solution that is 30% acid =  x + y

Amount of acid in that solution =  \frac{30}{100}(x+y) = 0.3x + 0.3y

The amount of acid in the solution that is 30% acid = Volume of acid in the solution that is 20% acid + Volume of acid in the solution that is 60% acid

0.3x + 0.3y = 0.2x + 0.6y

0.1x = 0.3y

\frac{x}{y} =  \frac{3}{1}

Hence, for every 1 part of 'y' we have 3 parts of 'x'.

The number of gallons of the 60 percent acid solution must be used to obtain 10 gallons of the 30 percent acid solution =  \frac{1}{4} * 10 = 2.5

Option B

ShilpiAgnihotrii · Answer

Use weighted avg formula to get ratio of 20% and 60% soln mixtures.

w1/w2 = 3/1

In 10 gallons 1/4th part is 2.5. Ans B

pakman95 · Answer

How are you guys getting the 1/4 * 10?

rfrederick1211 · Answer

its 1:3, the total is 4 parts, so its 1/4, if theres 2 parts in a ratio, lets say 1 part orange juice, 3 parts proseco, of the 4 parts, 1 part of the total 4 is orange juice,

Akshat_verma_25 · Answer

Now, it's clear. Thanks and kudos.

RC3 · Answer

It can also be done with alligation method

X Y
 20 60
 30
 30 : 10
which is 3:1
required gallons of Y solution are 1/4*10 = 2.5

A certain solution that is 30 percent acid is obtained by mixing x

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A certain solution that is 30 percent acid is obtained by mixing x

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