# Thread: Mixture story problem

1. ## 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?

2. ## Re: Mixture story problem

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

...
1. Using your labeling you already know:

$\left|\begin{array}{rcl}x+y&=&22.8 \\ 0.12x&=& 0.07(x+y) \end{array} \right.$

2. Solve for x and y. I've got $(x,y) = (13.3, 9.5)$

3. ## Re: Mixture story problem

Code:
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