Peter is renting two kinds of rafts for a vacation company. One type seats 3 people and the other seats 5 people. If 53 people are using the vacation
company and he rents 13 rafts, how many of each type of raft does he rent?

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.

4sqrt5

step-by-step explanation:

the base has dimensions of 8 x 4, so the diagonal is 64 + 16 square rooted or 4sqrt5.