# Help me Fast for a College Class!!!

• Jun 19th 2006, 06:13 PM
Brooke
Help me Fast for a College Class!!!
:) Question is: How many gallons of a solution of glycerine and water containing 55% glycerine should be added to 15 gallons of a 20% solution to give a 40% solution??
• Jun 19th 2006, 06:21 PM
ThePerfectHacker
Quote:

Originally Posted by Brooke
:) Question is: How many gallons of a solution of glycerine and water containing 55% glycerine should be added to 15 gallons of a 20% solution to give a 40% solution??

Begin, to knowing that,
$\displaystyle \mbox{concetration }=\frac{\mbox{volume of substance}}{\mbox{total volume}}$

Solution 1 has 55% of x gallons is glycerine which is $\displaystyle .55x$ gallons.
Solution 2 has 20% of 15 gallons is glycerine which is $\displaystyle .2\cdot 15=3$ gallons.
Thus when you combine them,
you have $\displaystyle .55x+3$ is amount of glycerine.
and, in total you have,
$\displaystyle x+15$
And you want 40% thus,
$\displaystyle \frac{.55x+3}{x+15}=.4$
Thus,
$\displaystyle .55x+3=.4(x+15)$
Thus,
$\displaystyle .55x+3=.4x+6$
Thus,
$\displaystyle .15x=3$
Thus,
$\displaystyle x=20\mbox{ gallons}$