PS 1000: Section 6 # 19

[envyk10]

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

I got the answer by plugging in the values. Can somebody please suggest a better method.

Thanks

[bww]

Hi...is the answer 20/3?

[bww]

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

Let x be the amount of liters of pure alcohol that must be added. The % of alcohol of this x liters is 100%, or 1. Thus, the total amount of liters that must be added is 1x.

We already have 100 liters of the 20% alcohol solution. Thus, the total amount of liters that we already have is .20(100) or 20.

The solution we want is 100+x (what we already have + what we need) that is 25% alcohol. Thus, the total amount of liters combined is .25(100+x).

Put the three together: 1x+20=.25(100+x) and solve for x.

[envyk10]

Yes, the answer is C. 20/3

[Cybermusings]

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

20% of 100-liter = 20 liter of pure alcohol
(20+x)/(x+100) * 100 = 25
2000 + 100x = 25x + 2500
500 = 75x
x = 500/75 = 20/3..