3 litres of orange concentrate were mixed with 5 litres of water to make a
drink. Later, 2 litres of orange were mixed with 3 litres of water. Which mix is more concentrated? Consider the following strategy. To compare
3 Orange and 5 Water with 2 Orange and 3 Water

remove the second from the first and compare

1 Orange and 2 Water with 2 Orange and 3 Water.

Remove the first from the second and compare

1 Orange and 2 Water with 1 Orange and 1 Water.

Now you can see that the second was the more concentrated.

Will this strategy always work?

My attempt: 

First I used examples to test this strategy by comparing 4 litres of orange concentrate with 5L of water with 2L of orange concentrate with 3L of water. 

By subtracting the second from the first I have, 2L of orange and 2 L of water with 2 L of organ and 3 litres of water. 

Now I subtract the the first from the second which results to 2L of orange with 2L of water compared to 0 litres of orange with 1 litre of water. 

This shows that the first is more concentrated because either the orange or the water from the remaining ratio is not zero. 

I tried to prove if this strategy works more generally by setting up ratios with variables but I can't seem to prove why this strategy works. 

Can anyone help?