Question

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 How many canoes will the group need? Write equations with unknowns to show your steps

Answer 1

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:

$3x=273..(1)$

$3x+2y=485..(2)$

Upon substituting equation 1 in equation 2 we will get,

$273+2y=485$

$2y=485-273$

$2y=212$

$y=\frac{212}{2} =106$

Therefore, number of 2 seater canoes will be 106.

Upon solving our 1st equation we will get number of 3 seater canoes.

$3x=273$

$x=\frac{273}{3} =91$

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.

$\text{Total canoes needed}=106+91=197$

Therefore, group will need 197 canoes.