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.

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

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

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

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

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

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

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

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!