Question

An elevated can hold less than 2700 pounds of extra weight. If an average person weighs 150 pounds, what is the maximum. number of people that can be on the elevator at one time.

Answer 1

It is said that the elevator can hold LESS THAN 2700 pounds of extra weight. This means:

`\text{weight}<2700`

You're also given how much an average person weights: 150 pounds.

The weight inside the elevator is the sum of all people inside of it. You don't know exactly how many people are in the elevator. You know that each person there weights around 150 pounds, so you just say 'ok, I'll assume that every person in the elevator weights 150 pounds'. This will make calculations much easier.

So if the weight inside the elevator is the sum of all the weights of each person inside the elevator, and every person weights the same (150 pounds) then, instead of adding one by one you can multiply the weight of one person by the total number of people there:

`\text{weight}=\text{people}*150pounds`

Let's represent 'people' with the letter 'p'. So, if we put this new expression into the first one (the one that gives you the maximum weight the elevator can hold) we have this new one:

`p*150pounds<2700pounds`

If we want to know how many people can the elevator hold, we would clear 'p' from here:

`p<(2700pounds)/(150pounds)`

Solving:

`p<18`

This means that the elevator can hold less than 18 people with average weight (150 pounds)