Let b be the number of backpacks with tent and w be the number of warm hiking clothes they rent. Since they in total rent 16 items, we can write the first equation as:
We also know that the hikers spend $256 to rent equipment from Norgay High Altitute Hiking. Additionally, a backpack+tent, b, costs $25 and a set of warm hiking clothes, w, costs $13. We can write this as the equation:
Combining the equations, we have the following system of equations:
To find how many backpack+tents and how many sets of warm hiking clothes the group of hikers rent, we have to solve the system
for b and w. We will use the substitution method. In order to use it, we need one of the variables isolated. Let's isolate b in Equation (I).
Now we can substitute 16−w for b in Equation (II) and solve the resulting equation for w.