Chapter 7.2, Problem 43WE

To determine

The numerical value of the ratio $a:b$

Answer to Problem 43WE

The required value of ratio is $a:b=3:2$

Explanation of Solution

Given information:

It is given $\frac{4a-9b}{4a}=\frac{a-2b}{b}$

Given $\frac{4a-9b}{4a}=\frac{a-2b}{b}$

Dividing numerator and denominator by b on both sides

  $\begin{array}{l}\frac{\frac{4a-9b}{b}}{\frac{4a}{b}}=\frac{\frac{a-2b}{b}}{\frac{b}{b}}\\ \frac{\frac{4a}{b}-9}{\frac{4a}{b}}=\frac{\frac{a}{b}-2}{1}\end{array}$

Let $\frac{a}{b}=t$ and solving for t

  $\begin{array}{l}\frac{4t-9}{4t}=t-2\\ 4t-9=4t^2-8t\\ 4t^2-12t+9=0\end{array}$

Using quadratic formula

  $\begin{array}{c}t=\frac{12\pm \sqrt{144-144}}{8}\\ =\frac{12\pm 0}{8}\\ =\frac{3}{2}\end{array}$

The required value of ratio is $a:b=3:2$