There is an order of 400ml of 0.50% of solution. You have in stock 16 oz. bottle of 0.75% and 16 oz. bottle of 0.35%. How much of each do you need to mix together. I know the answer is 150ml of .75% and 250ml of .35% but don't know how to get it.

Question

There is an order of 400ml of 0.50% of solution.  You have in stock 16 oz. bottle of 0.75% and 16 oz. bottle of 0.35%.  How much of each do you need to mix together.  I know the answer is 150ml of .75% and 250ml of .35% but don't know how to get it.

whpalmer4 · Answer

You need 400 ml of 0.5% solution.  How much of the substance of interest is present in that?

whpalmer4 · Answer

400 ml * 0.5% * 1/100% = 2 ml

Now, if we use $a$ to represent the quantity of $0.75\%$ stock solution, and $b$ to represent the quantity of $0.35\%$ stock solution, the amount of the SOI contributed by $a$ is $0.75*0.01*a = 0.0075a$ and similarly for $b$ it is $0.35*0.01*b = 0.0035b$.

Together, the two add up to contribute 2 ml to the final solution, so 
$$0.0075a + 0.0035b = 2$$

Also, we know that we are going to make 400 ml of solution from $a$ and $b$, so 
$$a+b = 400$$

That gives us two equations in two unknowns:

$$0.0075a + 0.0035b = 2$$$$a+b=400$$To make this a bit easier, I would get rid of the decimals by multiplying the first equation by 1000:

$$1000*0.0075a + 1000*0.0035b = 1000*2$$$$75a+35b = 2000$$

Next, solve the other equation for one variable in terms of the other:
$$a = b-400$$
Now substitute the right hand side of that wherever you see the left hand side of that in the first equation:
$$75a+35b=2000$$$$75(b-400) + 35b = 2000$$
I'm confident you can solve that equation for $b$.  Then plug your value obtained for $b$ into $a = b-400$ and find $a$.

anonymous · Answer

I will work on it and see what I get  thanks

whpalmer4 · Answer

uh don't follow my work exactly or you'll get it wrong :-)

$$a+b = 400$$$$a = 400-b$$not $a = b-400$!

whpalmer4 · Answer

Geez, I really didn't do well here, there's another mistake, too :-(

multiply first equation by 10000, not 1000:
$$75a+35b=20000$$

anonymous · Answer

reworking it still

anonymous · Answer

not getting correct answer.  This is what I have so far.
75(400-b) +35b=20000
-75b+30000+35b=20,000
-40b=17,000
b=-425  (this can't be right  -not sure what is wrong)

whpalmer4 · Answer

$$75(400-b) + 35b = 20000$$$$30000-40b = 20000$$$$10000=40b$$

anonymous · Answer

got it   subtrated 3,000 instead of using 30,000  thanks