Question

Peter is renting two kinds of rafts for a vacation company. One type seats 3

Answer 1

Answer:

Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.

Step-by-step explanation:

Let $x$ denote the number of rafts seating 3 people and $y$ the number of rafts seating 5 people. The total number of rafts is 13, so $x+y=13$. 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 $3x+5y=53$.

It's always a good idea to put these equations under each other:

$\left \{ {{x+y = 13} \atop {3x+5y=53}} \right.$

We can subtract the first equation three times from the second one to obtain $(3x+5y)-3(x+y) = 53 - 3(13)\\3x-3x + 5y - 3y = 53 - 39\\2y = 14\\y=\frac{14}{2} = 7$

Now, substitute this found value for $y$ into $x+y = 13$ and we see that $x=6$. We are now done: Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.