Chapter 8.1, Problem 11GP

To determine

An equation and how much it weighs on earth

Answer to Problem 11GP

The equation as $\frac{1}{6}x=54$

The weight on Earth is $x=324$ .

Explanation of Solution

Given:

The weight of an object on the Moon is one-sixth its weight on the Earth and if an object weighs 54 pounds

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find the equation here weight of an object on the Moon is one-sixth its weight on the Earth. Let x be the weight of an object on Earth

The weight of an object on the moon is $\frac{1}{6}x$

Object weight on the moon is $54\text{pounds}$

Thus, we can write an equation as $\frac{1}{6}x=54$

Then find the value of x as below:

  $\begin{array}{c}\frac{1}{6}x=54\\ \frac{1}{6}x\times 6=54\times 6\\ x=324\end{array}$

Thus, the weight on Earth is $x=324$ .