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) $\dfrac{5}{3}=\dfrac{40}{w}$

The mass of shorter bar = 24 kg

Step-by-step 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 :-

$\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}$

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 :-

$\dfrac{\text{Mass of shorter bar}}{\text{length of shorter bar}}=\dfrac{\text{Mass of longer bar}}{\text{length of longer bar}}\\\\\Rightarrow \dfrac{w}{3}=\dfrac{40}{5}$

It can also be written as :

$\dfrac{5}{3}=\dfrac{40}{w}$

When we solve this , we get

$w=\dfrac{40\times3}{5}=24$

Hence, the mass of shorter bar = 24 kg