Thread: Monday Morning Brain Wake-up

So it's Monday and it's time to wake the brain for the week so try solving this and show how you did it.

suppose you work in a lab. You need a 15% acid solution for a certain test, but your supplier only ships a 10% solution and a 30% solution. Rather than pay the hefty surcharge to have the supplier make a 15% solution, you decide to mix 10% solution with 30% solution, to make your own 15% solution. You need 10 liters of the 15% acid solution. How many liters of 10% solution and 30% solution should you use?

I used to do a lot of these in school, so I do have an answer, but I'm keeping schtum so I dont give an answer in the first post..!

I've sent you a PM though Nelson.

It didn't work, my brain is still asleep

You do not provide enough information to solve the problem. Specifically, you say you have 10% and 30% solutions and you want a 15% solution, but you do not say if this is percent by weight or volume. If, however, we assume it is by volume, then the problem is easy:

Let X = the number of liters of 30% solution

Then

10*0.15 = x*0.30+(10-x)*0.10

1.5=.3x+1.0-0.1X

0.2x=0.5

x = 2.5 liters of 30% solution
Thus:

2.5 liters of 30% solution
and
7.5 liters of 10% solution

If the percentages are, however, by weight the problem is more complicated and you will need to have the densities of the various solutions.

Originally Posted by MasterRolf

If the percentages are, however, by weight the problem is more complicated and you will need to have the densities of the various solutions.

That didn't work either. I'm even sleepier now than I was

Originally Posted by MasterRolf

You do not provide enough information to solve the problem. Specifically, you say you have 10% and 30% solutions and you want a 15% solution, but you do not say if this is percent by weight or volume. If, however, we assume it is by volume, then the problem is easy:

Let X = the number of liters of 30% solution

Then

10*0.15 = x*0.30+(10-x)*0.10

1.5=.3x+1.0-0.1X

0.2x=0.5

x = 2.5 liters of 30% solution
Thus:

2.5 liters of 30% solution
and
7.5 liters of 10% solution

If the percentages are, however, by weight the problem is more complicated and you will need to have the densities of the various solutions.

That's a lot prettier than my solution.

I figured that if 30-10= 20 (diff between solutions), and you only wanted to increase by 5, you needed a 3:1 ratio, 10% to 30%.

3:1 means you'll be working in sets of 4 (3+1), and your total is 10, so I calculated that 4 goes into 10 2.5 times.

Therefore:

3:1 -> 3(2.5): 1(2.5) -> 7.5:2.5 (10% to 30%)

Now that I've made all the mathematicians on the forum cry for the day, back to work.

Vulcan rider has the solution.

Stubear got the correct answer right off the bat.

Originally Posted by thebigspendur

Vulcan rider has the solution.

Stubear got the correct answer right off the bat.

And in so much as I posted my answer before Vulcan, I do as well.

Originally Posted by MasterRolf

And in so much as I posted my answer before Vulcan, I do as well.

That's OK. I'm not greedy; I can share a victory. Thanks for making me think a bit, thebigspendur!

you guys are geniuses.. i read the problem and all i could think was how they managed it in die hard 3.