Chapter 4.6, Problem 23HP

To determine

To find: the age of E

Answer to Problem 23HP

The age of E is 24 years.

Explanation of Solution

Given:

One personEtakes three-fourths of her age and adds 9.

And takes one-fourth of her age and adds 21.

Finds that the above two conditions are equal.

Calculation:

The objective is to find the age of Emelia.

Let the age of E is x.

Here, $\frac{3}{4}$ of the age is $\frac{3}{4}x$

Add 9 to get $\frac{3}{4}x+9$

And $\frac{1}{4}$ of the age is $\frac{1}{4}x$

Add 21, $\frac{1}{4}x+21$

Compare both equations to find out the value of x .

  $\begin{array}{l}\frac{3}{4}x+9=\frac{1}{4}x+21\\ \frac{3}{4}x+9-\frac{1}{4}x-9=\frac{1}{4}x+21-\frac{1}{4}x-9\text{ Subtract }\left(\frac{1}{4}x+9\right)\text{on both sides}\\ \frac{3}{4}x-\frac{1}{4}x=21-9\text{ Simplify}\\ \frac{2}{4}x=12\text{ Subtract}\\ \frac{1}{2}x=12\\ 2\times \frac{1}{2}x=12\times 2\text{ Multiply 2 on both sides}\text{.}\\ x=24\end{array}$

Hence, the age of E is 24 years.

Conclusion:

Hence, the age of E is 24 years.