Question

Mandy works construction. She knows that a 5 meter long metal bar has a mass of 40 kg. Mandy wants to figure out the mass (w) of a bar made out of the same metal that is just 3 meters long and the same thickness. Which proportion could Mandy use to model out this situation?

A: 40/3=w/5
B:5/3=40/w

Solve the proportion to determine the mass of the shorter bar.

Answer 1

I think neither of these proportions are right... are you sure you wrote it down correctly?

Answer 2

Answer: B)
`(5)/(3)=(40)/(w)`

The mass of shorter bar = 24 kg

Explanation:

We assume that the mass of the metal bar is directly proportional to its length.

We know that the equation to shows direct variation between two quantities is given by :-

`(x_1)/(y_1)=(x_2)/(y_2)`

Given : Mandy works construction. She knows that a 5 meter long metal bar has a mass of 40 kg.

Mandy wants to figure out the mass (w) of a bar made out of the same metal that is just 3 meters long and the same thickness.

For the given situation the direct variation equation will be :-

`\frac{\text{Mass of shorter bar}}{\text{length of shorter bar}}=\frac{\text{Mass of longer bar}}{\text{length of longer bar}}\\\\\Rightarrow (w)/(3)=(40)/(5)`

It can also be written as :

`(5)/(3)=(40)/(w)`

When we solve this , we get

`w=(40*3)/(5)=24`

Hence, the mass of shorter bar = 24 kg