Alligation of solutions - creating the unavailable

Sometimes in clinical practice, the ideal solution to administer to a patient, or to use for a process, is either unavailable or does not exist. In some circumstances, we may be able to create a solution from existing, available products. In the most simple circumstances, we may be able to use water to dilute a solution to an appropriate concentration, but there are often situations where it may be easier to mix different weight per volume (w/v) concentration solutions to produce an appropriate final product.

The following scenario considers a situation in which a solution of 17.5% glucose is needed, but the only materials available are 10% and 50% glucose.

Were we to dilute this amount of 50% glucose to 500 ml with water, a suitable solution would be achieved. However, in the absence of water, we can use 10% glucose instead.

Your answer from Question 2 is clearly not close to the desired 17.5%, so a straightforward dilution like this is not a viable way to make this solution. It is apparent that, since our diluent contains a higher concentration of glucose than pure water, the more glucose solution we add as a diluent, the less 50% glucose we must start with in order to not end up with a final solution with a concentration above target. We can achieve this by producing a ratio of the differences between the starting