Hello arch

Welcome to Math Help Forum!You don't give us any quantity of the original mixture, but let me assume that there's 1 litre, and show you how to do that. Then you can work out how to do it for any other volume.

In 1 litre of the mixture, 13%, or 0.13 litre, is y. We want to add a quantity of x so that this 0.13 litre is 0.5% of the new total volume. If we add litres of x, the new total volume is litres, and 0.5% of this is . So we have:

So for every litre of the original mixture, we must add 25 litres of x, in order to make the new mixture 99.5% x, 0.5% y.

Grandad