At Bo's Boat Shop, all kayaks have the same number of seats and all rowboats have the same number of seats. A kayak has fewer seats than a rowboat. Two kayaks and two rowboats have a total of \(10\) seats. One kayak and three rowboats have a total of \(11\) seats.
How many seats are in one kayak?
Since two kayaks and two rowboats have a total of \(10\) seats, then half as many kayaks and rowboats will have half as many seats. That is, one kayak and one rowboat will have a total of \(10\div 2 = 5\) seats.
Since a kayak has less seats than a rowboat, then it must be the case that one kayak has \(1\) seat and one rowboat has \(4\) seats, or that one kayak has \(2\) seats and one rowboat has \(3\) seats.
If one kayak has \(1\) seat and one rowboat has \(4\) seats, then one kayak and three rowboats have \(1+4+4+4=13\) seats. Since we’re told that one kayak and three rowboats have \(11\) seats, this is not a possible solution.
If one kayak has \(2\) seats and one rowboat has \(3\) seats, then one kayak and three rowboats have \(2+3+3+3=11\) seats. Since we’re told that one kayak and three rowboats have \(11\) seats, this is a possible solution.
Thus, \(2\) seats are in one kayak.