How many liters of pure alcohol must be added
to a 100-liter solution that is 20 percent alcohol
in order to produce a solution that is 25 percent
alcohol?
(A) 7/2
(B) 5
(C) 20/3
(D) 8
(E) 39/4
OA C
Please explain. Thanks.
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DanaJ
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You currently have 20l of alcohol in your solution.
Next you add x l of pure alcohol, bringing the total amount of alcohol at 20 + x. Now, this 20 + x represents 25% or 0.25 of the new solution, which comes in at 100 + x (since you had 100l in the beginning and then added x l).
This means that 20 + x = 0.25(100 + x)
20 + x = 25 + 0.25x
0.75x = 5
x = 5/0.75 = 5*4/3 = 20/3
Next you add x l of pure alcohol, bringing the total amount of alcohol at 20 + x. Now, this 20 + x represents 25% or 0.25 of the new solution, which comes in at 100 + x (since you had 100l in the beginning and then added x l).
This means that 20 + x = 0.25(100 + x)
20 + x = 25 + 0.25x
0.75x = 5
x = 5/0.75 = 5*4/3 = 20/3
