Well, in chemistry, you deal with moles which maybe makes it easier to understand, but I'll talk about mass here as an analogy to help you.

Let 1 L of solution has a mass of 1 kg.

Let's say the concentrations given are concentrations by mass, meaning that 15% is similar to saying 15% by mass of the 1L solution is salt. (ie, 0.15 kg of 1 kg of solution is salt)

0.15x will give the total mass of salt in x litres of 15% solution.

Similarly,

8% is similar to saying 8% by mass of the 1L solution is salt. (ie, 0.08 kg of 1 kg of solution is salt)

0.08(5) will give the total mass of salt in 5 litres of 8% solution.

As such,

10% is similar to saying 10% by mass of the 1L solution is salt. (ie, 0.1 kg of 1 kg of solution is salt)

0.1(y) will give the total mass of salt in y litres of 10% solution.

where y is the sum of volumes of both solutions.

This gives a sum of masses:

0.15x + 0.08(5) = 0.1(x + 5)

Note that it's not 0.18. This must have been a mistake, because two more dilute solutions cannot give a more concentrated one.