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Solution A is 40% chlorine by volume, and Solution B is 60% chlorine by volume. If a tank currently holds 40 gallons of

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Solution A is 40% chlorine by volume, and Solution B is 60% chlorine by volume. If a tank currently holds 40 gallons of

by BTGmoderatorDC » Wed Dec 30, 2020 4:36 pm

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Solution A is 40% chlorine by volume, and Solution B is 60% chlorine by volume. If a tank currently holds 40 gallons of Solution A, how many gallons of Solution B must be added so that the liquid in the tank is 50% chlorine?

A. 40 gallons
B. 50 gallons
C. 60 gallons
D. 80 gallons
E. 100 gallons



OA A

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Re: Solution A is 40% chlorine by volume, and Solution B is 60% chlorine by volume. If a tank currently holds 40 gallons

by swerve » Wed Dec 30, 2020 5:02 pm
BTGmoderatorDC wrote: ↑
Wed Dec 30, 2020 4:36 pm
 Solution A is 40% chlorine by volume, and Solution B is 60% chlorine by volume. If a tank currently holds 40 gallons of Solution A, how many gallons of Solution B must be added so that the liquid in the tank is 50% chlorine?

A. 40 gallons
B. 50 gallons
C. 60 gallons
D. 80 gallons
E. 100 gallons



OA A

Source: Veritas Prep
\(40A + 60B = 50A + 50B\)

\(10B = 10A\)

\(\dfrac{A}{B} = \dfrac{1}{1}\)

For \(1A\) added, there's \(1B\) added since the ratio is \(1\) to \(1\). So if \(40\) gallons of \(A\) is in the tank, \(40\) gallons of \(B\) will need to be added to maintain the ratio.

Therefore, A
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Re: Solution A is 40% chlorine by volume, and Solution B is 60% chlorine by volume. If a tank currently holds 40 gallons

by Scott@TargetTestPrep » Sat Jan 02, 2021 2:08 pm
BTGmoderatorDC wrote: ↑
Wed Dec 30, 2020 4:36 pm
 Solution A is 40% chlorine by volume, and Solution B is 60% chlorine by volume. If a tank currently holds 40 gallons of Solution A, how many gallons of Solution B must be added so that the liquid in the tank is 50% chlorine?

A. 40 gallons
B. 50 gallons
C. 60 gallons
D. 80 gallons
E. 100 gallons



OA A

Solution:

Currently there are 40 x 0.4 = 16 gallons of chlorine in solution A. We can let the amount of solution B = n and create the equation:

(16 + 0.6n)/(40 + n) = 1/2

2(16 + 0.6n) = 40 + n

32 + 1.2n = 40 + n

0.2n = 8

n = 40

Alternate Solution:

Notice that 50 is the average of 40 and 60. Notice that when an equal amount of 40% and 60% solutions are mixed, the resulting mixture will have a concentration of 50%. Thus, we should add as much 60% solution as the amount of 40% solution already in the tank (which is 40 gallons) to obtain a 50% chlorine solution.

Answer: A

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