Question

The weight M of an object on the moon varies directly as its weight E on earth. A person whoweighs 156.71 lb on earth weighs 26.64 lb on the moon. How much would a 213.53-lb personweigh on the moon?A 213.53-1b person would weigh___ lb on the moon. (Round to the nearest tenth.)

Answer 1

Since the weight varies directly, we have that

`156.71=k*26.64`

where k is the constant of proportinality.

In order to find k, we can divide both sides by 26.64 and get

`\begin{gathered} (156.71)/(26.64)=k \\ or\text{ equivalently, } \\ k=(156.71)/(26.64) \end{gathered}`

which gives

`k=5.8825`

Once we know the constant of proportionallity, we can write

`213.53=k* x`

where x denotes the unknown weight on the Moon. Since k is 5.8825, we get

`213.53=5.8825* x`

Then, by dividing both sides by 5.8825, we obtain

`\begin{gathered} (213.53)/(5.8825)=x \\ or\text{ equivalently,} \\ x=(213.53)/(5.8825) \end{gathered}`

Therefore, we have

`x=36.299\text{ lb}`

Finally, by rounding to the nearest tenth, the answer is: 36.3 lb