Answer:
Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.
Step-by-step explanation:
Let denote the number of rafts seating 3 people and the number of rafts seating 5 people. The total number of rafts is 13, so . We can also assume that every raft is filled to the brim (it isn't stated explicitly though, but it's probably the intention of the question maker), so .
It's always a good idea to put these equations under each other:
We can subtract the first equation three times from the second one to obtain
Now, substitute this found value for into and we see that . We are now done: Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.
If r(x) is an inverse of s(x), then we know that r(s(x)) = x and s(r(x)) = x.
Let's think about what inverses are in order to help us understand.
We know that a function, in order to be an inverse of another, has to be reflected about the y = x line.
So, if a function is reflected about the y = x line, then if we have a composite function, they will always result in the same input (ie x)