Question

How much water must be added to 12 L of a 40% solution of alcohol to obtain a 30% solution?

A. .5 L
B. 5 L
C. .4 L
D. 4 L

Answer 1

How many liters of alcohol did you start with?

Answer 2

(hint: 40% of 12)

Answer 3

I'm confused...

Answer 4

The concentrations, 40%, 30% are fractions of alcohol-over-water.

Answer 5

40% alcohol means it is 40 parts alcohol to 100 parts total solution of alcohol+water.
So if the concentration is 40% then 40% of the 12 liters is the liters of alcohol in the solution.

Answer 6

^^ *(sorry, should say, "The concentrations, 40%, 30% are fractions of alcohol volume -over- total volume (alcohol+water).")

Answer 7

You're starting with 40%, 40% = 4/10, so
\[\large \frac{4}{10}=\frac{liters \space of \space alcohol}{total \space volume}\]

Answer 8

0.4?

Answer 9

You want 30%, 30% = 3/10, so
\[\large \frac{3}{10}=\frac{liters \space of \space alcohol}{12+x \space liters}\]

Answer 10

Yes, 0.4 means the same as 40%, which means the same as 4/10, you can express that fraction however you want.
So, if the total volume you start with is 12 liters, how many of those liters are alcohol?