:) 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??

please answer me!!! :confused:

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- Jun 19th 2006, 06:13 PMBrookeHelp 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??

please answer me!!! :confused: - Jun 19th 2006, 06:21 PMThePerfectHackerQuote:

Originally Posted by**Brooke**

$\displaystyle \mbox{concetration }=\frac{\mbox{volume of substance}}{\mbox{total volume}}$

**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,

$\displaystyle x=20\mbox{ gallons}$