# Thread: word problem;

1. ## word problem;

how many liters of a 25%alcohol solution must be mixed with a 12% solution to get 13 liters of a 15% solution.

i have always had trouble interpreting math problems. once i get pushed in the right direction, im pretty sure i will be able to solve the equation.
pleasee and thank youu!

2. Hello, annabananzaa!

How many liters of a 25% alcohol solution must be mixed with a 12% solution
to get 13 liters of a 15% solution.?
These "mixture problems" can be solved if we organize our facts.

Let $x$ = liters of 25% solution.
Then $13-x$ = liters of 12% solution.
(I hope you see why.)

The $x$ liters of 25% solution contains: . $0.25x$ liters of alcohol.

The $13-x$ liters of 12% solutions contains: . $0.12(13-x)$ liters of alcohol.

. . Hence, the mixture will contain: . $0.25x + 0.12(13-x)$ liters of alcohol. .[1]

But we know that the final mixture will be 13 liters which is 15% alcohol.
. . It will contain: . $0.15(13) \:=\:1.95$ liters of alcohol. .[2]

We just described the final amount of alcohol in two ways.
There is our equation! . . . Equate [1] and [2]

. . . . $0.25x + 0.12(13-x) \;=\;1.95$

Got it?

3. yess! i get it!

its always the wording and translation into a equation that i have problems with.

thank you so much for taking out the time to explain it to me!