Answer:
Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.
Step-by-step explanation:
Let [tex]x[/tex] denote the number of rafts seating 3 people and [tex]y[/tex] the number of rafts seating 5 people. The total number of rafts is 13, so [tex]x+y=13[/tex]. 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 [tex]3x+5y=53[/tex].
It's always a good idea to put these equations under each other:
[tex]\left \{ {{x+y = 13} \atop {3x+5y=53}} \right.[/tex]
We can subtract the first equation three times from the second one to obtain [tex](3x+5y)-3(x+y) = 53 - 3(13)\\3x-3x + 5y - 3y = 53 - 39\\2y = 14\\y=\frac{14}{2} = 7[/tex]
Now, substitute this found value for [tex]y[/tex] into [tex]x+y = 13[/tex] and we see that [tex]x=6[/tex]. We are now done: Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.
