Chapter 8.3, Problem 23HP

To determine

How old is Emelia

Answer to Problem 23HP

The age of Emelia is $x=24$

Explanation of Solution

Given:

Emelia discovered that if she takes three-fourths of her age and adds 9, it produces the same results as when she takes one-fourth of her age and adds 21

Concept Used:

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.

In order to find an equation

Let x be the age of Emelia.

Three-fourths of her age and adds 9 is equivalent to one fourth of her age and adds 21

The equation as shown below,

  $\frac{3}{4}x+9=\frac{1}{4}x+21$

Thus, the equation is $\frac{3}{4}x+9=\frac{1}{4}x+21$

In order to solve the equation $\frac{3}{4}x+9=\frac{1}{4}x+21$ , first subtract both sides by $9$ and then subtract both sides by $\frac{1}{4}x$ and then multiply both sides by $2$ and then simplify as below:

  $\begin{array}{c}\frac{3}{4}x+9=\frac{1}{4}x+21\\ \frac{3}{4}x+9-9=\frac{1}{4}x+21-9\\ \frac{3}{4}x=\frac{1}{4}x+12\\ \frac{3}{4}x-\frac{1}{4}x=\frac{1}{4}x+12-\frac{1}{4}x\\ \frac{2x}{4}=12\\ \frac{x}{2}=12\\ \frac{x}{2}\times 2=12\times 2\\ x=24\end{array}$

Thus, the age of Emelia is $x=24$