## Alligation math with water problem

by Sheila

(Dunwoody, GA)

I am studying for the PTCB exam and came across this question.

**How much water should be added to 95% ethanol to make 1L of a 30% solution?**

I thought it was an alligation problem, but when I work through the problem I do not get the answer that goes with the question. I was thinking the 95% is the higher strength, 0% strength for the water, the desired quantity is 1000 ml and the desired strength is 30%. After the calculations I get 205 ml of water. The answer is suppose to 75 ml. Please show me the math. Thanks.

**Reply (by Keith)**
Hi Sheila, from the information provided in the question, it can definitely be solved using an Alligation tic-tac-toe grid. But, let's first take a step back for a moment and think about the question vs the answer provided.

If you took a 95% concentration and diluted it in half, in this case, that would be 500mL of each. That would give you (half of 95) a 47.5% solution, which is still too high, right, and even more water would be required. So right off the bat, you already know the answer's gotta be over 500mL.

If you're working that problem out of a book, don't be too shocked if the answer key is wrong. It is annoying, but all books seem to have a level of errors in their answer keys.

Anyhow, What I'm trying to convey about the

**half and half** method I mentioned above is to use some techniques to shape up math questions before your pencil even touches the paper. Having a starting point will help you to get through the problem. Process of elimination will help you in many situations.

I suggest trying the problem over again using alligation to solve it.

I've put together some choices for you here to make it easier.

How much water should be added to 95% ethanol to make 1 L of a 30% solution?

A. 685mL of 95% + 316mL of SWFI

B. 600mL of 95% + 400mL of SWFI

C. 316mL of 95% + 685mL of SWFI

D. 590mL of 95% + 410mL of SWFI