SOLUTION: How do I dilute a 70% peroxide solution to a 35% solution then to a 3.5% solution using 250 ml of the 70% solution

250 ml of the 70% solution contains 175 ml of peroxide and the rest water.

(That's because 70% of 250 ml is 175)

We will now add x ml of water.

Then there will still be only 175 ml of peroxide but there will be a total of
250+x ml of liquid altogether.

We therefore want the 175 ml of peroxide to equal 35% of the total 250+x ml 
of liquid, so

                  175 = 0.35(250+x)

Solve that and get x = 250 ml of water is to be added. 

So the answer to the first part of the problem is 

"Add 250 ml of water".

{Note: It makes sense that we would have to double the amount of liquid 
since 35% is exactly half of 70%. Therefore we could have reasoned out 
that the answer would be 250 ml of water without doing any algebra, since 
we started with 250 ml of solution and needed to double it to make it half
strength!]

Second part of question:

Now that we have added 250 ml of water to the 250 ml of solution, we now
have 500 ml of solution of which still only 175 ml is peroxide and the rest
water.

We will now add y ml of water.

Now there will still be only 175 ml of peroxide but there will be a total 
of 500+y ml of liquid altogether.

We therefore want the 175 ml of peroxide to equal 3.5% of the total 500+y
of liquid, so

                  175 = 0.035(500+x)

Solve that and get x = 4500 ml of water is to be added.

So the answer to the second part of the problem is: 

"Add 4500 ml more water".  (You could call that 4.5 liters of water.)

Edwin