Question

A group of 485 people take a canoe trip. They fill up all avalible 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 unknown to show your steps.

Answer 1

They will need 197 canoes.

Explanation:

The first step is to find the ''3-people canoes'' that they filled.

Given that 273 people filled a certain number ''a'' of canoes that each hold 3 people, we know that is we multiply the number of canoes ''a'' by the number of people that can each canoe hold, we will obtain the number of people who

will take the canoe trip in the ''3-people canoes''. We write :

`3a=273` ⇒

`a=(273)/(3)=91`

We find that
`a=91` canoes. This means that 91 ''3-people canoes'' were filled each one with 3 people in order to hold 273 people in total.

The second step is to find the remaining people that won't take the ''3-people canoes''. We do this by subtracting 273 people to the total 485 people.

`485-273=212`

We know that 212 people will travel in the ''2-people canoes''. Using a similar reasoning and defining as ''b'' to the total number of ''2-people canoes'' we write :

`2b=212\\b=(212)/(2)=106\\ b=106`

We find that
`b=106` canoes is the total number of ''2-people canoes'' that we need If we want them to be filled up with 212 people.

The total number of canoes that the group will need is the sum of ''3-people canoes'' and ''2-people canoes'' :

`Total=a+b=91+106=197`

The group of 485 people will need 197 canoes.

Answer 2

Answer:
3c=273
c=91
2c= 212
C= 106
c= 91+ 106= 197
so they will need 197 canoes total

Why:
So first you have to determine a set variable to represent the number of canoes, I chose C. Then you make an equation to represent the number of canoes 273 people will use if they group into 3's, from this I got 3c=273. Solve for C and get 91.
The remainder of the group which is 485-273= 212 will use canoes in groups of 2's. To represent this, 2c=212. Solve for C and get 106. Combine 106 and 91 to get the total number of canoes.