# Mixture story problem

• Apr 3rd 2012, 08:19 PM
Kibbygirl
Mixture story problem
Trying to learn how to do these types of problems. The last one I had for homework was wrong.

How much 12% Na2SO4 and pure water must be mixed to produce 22.8 gallons of a mixture that is 7% sodium sulfate?

I started with: Let x = the # of gallons of 12% Na2SO4
And Let y = the # of gallons of 100% water

Now I thought I do (value)(quantity).

I plugged:
(0.12)(x)+ (0.100)(w) = (0.07)(22.8)

and then I distributed -

0.12x+0.100w=1.596

Now I am not sure if that is correct. And if it is, I am stuck on what to do next?
• Apr 3rd 2012, 10:13 PM
earboth
Re: Mixture story problem
Quote:

Originally Posted by Kibbygirl
Trying to learn how to do these types of problems. The last one I had for homework was wrong.

How much 12% Na2SO4 and pure water must be mixed to produce 22.8 gallons of a mixture that is 7% sodium sulfate?

I started with: Let x = the # of gallons of 12% Na2SO4
And Let y = the # of gallons of 100% water

...

$\left|\begin{array}{rcl}x+y&=&22.8 \\ 0.12x&=& 0.07(x+y) \end{array} \right.$
2. Solve for x and y. I've got $(x,y) = (13.3, 9.5)$
a  @ x b  @ y ======== a+b @ z z = (ax + by) /(a+b) a      @ 12 22.8-a @  0 =========== 22.8  @  5 5 = (12a + 0) / 22.8 a = 13.3