We have been given that a group of 485 people take a canoe trip. They fill up all available canoes that each hold 3 people with 273 people. The rest of the group will ride in canoes that each hold 2 people.
Let x be number of 3 seater canoes and y be number of 2 seater canoes.
Upon using our given information we can set two equations as:
[tex]3x=273..(1)[/tex]
[tex]3x+2y=485..(2)[/tex]
Upon substituting equation 1 in equation 2 we will get,
[tex]273+2y=485[/tex]
[tex]2y=485-273[/tex]
[tex]2y=212[/tex]
[tex]y=\frac{212}{2} =106[/tex]
Therefore, number of 2 seater canoes will be 106.
Upon solving our 1st equation we will get number of 3 seater canoes.
[tex]3x=273[/tex]
[tex]x=\frac{273}{3} =91[/tex]
Therefore, number of 3 seater canoes will be 91.
To find total number of canoes we will add number of 2 seater and 3 seater canoes.
[tex]\text{Total canoes needed}=106+91=197[/tex]
Therefore, group will need 197 canoes.
