Question 1011852
I'm a 66 year old man with a debate with my wife.  I say the mixture would be 4 to 1 she disagrees. A 40% solution is to be mixed with water how much water is needed to make the solution 10%?
<pre>Sorry, sir, you're wrong! I assume you merely did a ratio of 40%:10% to get 4:1, but it doesn't work like that 
I don't know what your wife's ratio is, but yours is incorrect.

Let original amount of solution be S, and amount of water to add, W
Let's assume that the S units of solution contains .6S water 
Water + water = water
Then we get: .6(S) + W = .9(S + W) ---- Amounts of water in original solution and new solution are: .6, and .9, respectively 
.6S + W = .9S + .9W
W – .9W = .9S - .6S
.1W = .3S
W, or amount of water to add = {{{.3S/.1}}}, or 3S. 
This means that the amount of water to be added is 3 times the amount of the original solution. 

Now, the solution consists of 4S (S + 3S), of which 3S units of water were added to the original .6S units of water, which results in 3.6S units of water.
This makes the ratio: 3.6S:.4S, or {{{highlight_green(9:1)}}}