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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.