Chapter 9.7, Problem 14P

To determine

To solve: the system of equations in two variables.

Answer to Problem 14P

The age of Marion is 12 years old now and age of Les is 16 years old now .

Explanation of Solution

Given information:

Marion was $\frac{2}{3}$ as old as Les was. Now she is $\frac{3}{4}$ as old as he is .

Formula used:

Age problem.

Step1. The problem asks for the Bob’s age and Claire’s age now.

Step2. Let b = the Marion’s age .

Let c = the Les‘s age .

Step3. Use the facts of the problem to write two equations.

Step4. Solve the equations.

Calculation:

Consider ,

Let b = the Marion’s age .

Let c = the Les’s age .

Age	Four year ago
Marion	$b-4$
Les	$c-4$

According to the equation,

  $\begin{array}{l}=b-4=\frac{2}{3}(c-4)\\ =3(b-4)=2(c-4)\\ =3b-12=2c-8\\ =3b-12-2c+8=0\\ =3b-2c-4=0\text{ (i)}\end{array}$

Also,

  $=b=\frac{3}{4}c\text{ (ii)}$

Substituting equation (i) in (ii)

  $\begin{array}{l}=3b-2c-4=0\\ =3\left(\frac{3}{4}c\right)-2c-4=0\\ =\frac{9}{4}c-2c-4=0\\ =\frac{9c-8c-16}{4}=0\\ =c-16=0\\ =c=16\end{array}$

Putting value of c in equation (i) we get,

  $\begin{array}{l}=b=\frac{3}{4}(16)\\ =b=3(4)\\ =b=12\end{array}$

Hence, the age of Marion is 12 years old now and age of Les is 16 years old now .