Ok, this is a serious question. In orientation, we were told to wear insect repellent that’s at least 36% DEET. Now, I know, some people might be suspicious of chemicals. All I know is that malaria definitely kills people, so I’ll wear DEET on my feet to avoid it. Even though it melts my toenail polish. Which is serious-I wear sandals every single day here!
But, back to math. I have a 6 ounce bottles of bug spray with 25% DEET that I want to mix with a 1 ounce bottle of 100% DEET. I tried to figure out how much of the 100% stuff I should put into the 25% stuff, but I gave up. To all my math teachers, I’m really sorry, it’s not your fault. So, I’ve just been dumping both bottles together and figuring that it must be close. I won’t be able to tell you if you get it right or not, though, you’ll have to argue amongst yourselves. Please show all calculations for full credit.
My attempt:
1/4 ounce of 25% DEET
+
1/4 ounce of 25% DEET
+
1/4 ounce of 25% DEET
+
1/4 ounce of 100% DEET
Add the percents to get 175 and then divide by four, for the four portions added, and you get about 43%.
That makes a kind of sense to my mind. Not sure if I’m missing some big chunk of logic, though. I wasn’t nuts about math.
I would say use a ratio of 3 to 1 – 3 parts 25% DEET, 1 part 100% DEET.
Of course, since malaria hangs in the balance, please don’t go on my word alone!!
sorry, Nora, I was a liberal arts major
Okay in order to understand any type of dilution problem you need to understand the formula involved.
C1V1+C2V2=CfVf
where
C = concentration
V = volume
The problem is we will not know the final volume, and that would leave us with a complex formula to solve. But with a little creative plugging we find that a ratio of 4 parts of 25% + 1 part of 100% will yield 5 parts of 40% (so Eva was correct on the math for a 3:1 ratio). Going up to 5 parts of 25% + 1 part of 100% will yield 6 parts of 37.5%! As an aside 1 part to 1 part ratio will yield 2 parts of 62.5% solution. That may be a little too strong to use, although I have heard of people using 100% before. I would say to stick in the 3-4 parts of 25% to 1 part 100%.
OK, I was hilariously wrong. The non-hilarious part is that algebra will be required. Here’s a link to a site where you can do mixture calculations.
http://www.onlinemathlearning.com/mixture-problems.html#mix
I hereby am *not* “smarter than a 5th grader”!
Boats, I didn’t see your comment before I posted. Just wanted to add, YAY! Good job!
It is complicated set of formulas that creates a simply answer in the end. You have to divide the 25% can by the number of parts, add them together and square them. Add that sum to the bottle of 100%. That total is used to solve for variable X; which is your ounces needed to add. Take the first sum and multiply it by pie (3.14) which will give you and answer that you have to use fill in to the quadratic formula as variable C. this will give you an improper fraction that you have to multiply by the number of degrees in a right angle. Once you get that number…you then beg one of your friends to send you can of 36%!
kent, your answer cracked me up. I was halfway through it before I realized you weren’t serious…were you? Thanks for the answer Boats-I no longer feel guilty about forgetting how to figure this out-I never knew how to figure this out!!
I think I’ll stick to language stuff…
not the slightest idea what I was talking about. made it up as I went along. glad to put a smile on your face. 🙂