Chapter 8.5, Problem 26IP

To determine

Find the current age of Ang and Paula.

Answer to Problem 26IP

Present age of Ang is 15 years and Paula is 25 years.

Explanation of Solution

Given:

Five years ago Ang was $\frac{1}{2}$ as old as Paula. Now he is $\frac{3}{5}$ as old as Paula.

Complete the table shown below. Then use the table to write and solve an equation to find their current age.

Student	5 years ago	Now
Ang	$\frac{1}{2}a$
Paula	$a$	$a+5$

Concept Used:

Five years ago Ang was $\frac{1}{2}$ as old as Paula. Now he is $\frac{3}{5}$ as old as Paula.

According to the condition given, the current age of Ang is $\frac{3}{5}(a+5)$

5 years ago, the age of Ang was $\frac{1}{2}a$ , so after 5 years his age should be $\frac{1}{2}a+5$

The required Equation is: $\frac{1}{2}a+5=\frac{3}{5}(a+5)$

Calculation:

The required Equation is: $\frac{1}{2}a+5=\frac{3}{5}(a+5)$

Now solve for a:

Step 1: Multiply each term of both side by the LCM of 2 and 5 = 10

  $\begin{array}{l}\frac{1}{2}a+5=\frac{3}{5}(a+5)\\ 10·\frac{1}{2}a+10·5=10·\frac{3}{5}(a+5)[\text{Multiply each term by 10 ] }\\ 5a+50=6(a+5)\\ 5a+50=6a+30\\ 5a-5a+50=6a-5a+30[\text{Subtract 5a from both sides ]}\\ 50=a+30\\ 50-30=a+30-30[\text{Subtract 30 from both sides ]}\\ 20=a\Rightarrow a=20\end{array}$

Present age of Paula: a + 5 = 20 + 5 = 25 years.

Present age of Ang: $\frac{3}{5}(a+5)=\frac{3}{5}(20+5)=\frac{3}{5}(25)=15$

Present age of Ang is 15 years and Paula is 25 years.

Thus, the present age of Ang is 15 years and Paula is 25 years.