Answer:
A person weighing 100 lb on Earth will weigh 40 lb on Mars.
Step-by-step explanation:
Given:
The weight M of an object on Mars varies directly as it's weight E on Earth
[tex]M[/tex] represents weight of an object on Mars
[tex]E[/tex] represents weight of an object on Earth
So, it is given that [tex]M[/tex] directly varies with [tex]E[/tex].
[tex]M[/tex] ∝ [tex]E[/tex]
which can be written as
[tex]M=kE[/tex]
where [tex]k[/tex] represents the constant of proportionality.
Given a person weight 95 lb on Earth weighs 38 lbs on Mars.
So, we can evaluate [tex]k[/tex] using the given weights.
[tex]38=k(95)[/tex]
Dividing both sides by 95.
[tex]\frac{38}{95}=\frac{k(95)}{95}[/tex]
∴ [tex]k=\frac{38}{95}[/tex]
To find the weight of a person on Mars, given that he weighs 100 lb on Earth.
[tex]M=k(100)[/tex]
substituting value of [tex]k[/tex]
[tex]M=\frac{38}{95}\times 100[/tex]
[tex]M=\frac{3800}{95}[/tex]
∴ [tex]M=40\ lb[/tex]
Thus, a person weighing 100 lb on Earth will weigh 40 lb on Mars.
