Question

The weight of an object on the moon varies directly as the weight of the objects on Earth. A 90-pound object on Earth weighs 15 pounds on the moon. If an object weighs 156 pounds on Earth, how much does it weigh on the moon?

Answer 1

Hint: In order to solve this question, we will first find the ratio of the weight of an object on earth to the weight of the same object on the moon. Then we will get a relationship between them and then we will apply the same relationship to get the weight of the object on the moon when its weight on earth is 156 pounds.

Complete step by step answer:
We know that a 90-pound object on Earth weighs 15 pounds on the moon. Let us assume the weight of the object on the moon be \[{W_m}\] and the weight of an object on earth be ${W_e}$. So, the ratio of the weight of an object on earth to the weight of an object on moon will be,
$\dfrac{{{W_e}}}{{{W_m}}} = \dfrac{{15}}{{90}}$
On further solving, we get,
$\dfrac{{{W_e}}}{{{W_m}}} = \dfrac{1}{6}$
${W_e} = \dfrac{1}{6} \times {W_m}......(1)$
From the above equation we can say that the weight of an object on earth is one-sixth of the weight of an object on the moon.
So, in order to find the weight of an object on the moon, when its weight on earth is 156 pounds, we will simply find one-sixth the value of 156 pounds. So,
The weight of an object on moon $ = \dfrac{1}{6} \times 256$
On solving this, we get,
The weight of an object on the moon \[ = 26\]
Therefore, the weight of an object on the moon is 26 pounds when its weight on earth is 156 pounds.

Note:
We have solved this question by taking the fraction of the quantities given to us and then applying that fraction in the part which we have to calculate. But this question can also be solved by the unitary method. With the help of the unitary method, we will find the weight of an object on earth when its weight on the moon is 1 pound and with the help of this relation, we will find the required answer.