Chapter 9.7, Problem 19P

To determine

To solve: the system of equations in two variables.

Answer to Problem 19P

The age of Sean will be 10 years old and Lyle will be 20 years old.

Explanation of Solution

Given information:

Next year, Lyle will be twice as old as Sean will be. Four years ago, he was three times as old as Sean was.

Formula used:

Age problem.

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

Step2. Let b = the Lyle’s age .

Let c = the Sean‘s age .

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

Step4. Solve the equations.

Calculation:

Consider ,

Let b = the Lyle’s age now .

Let c = the Sean’s age now.

Age	Next year	Four years ago
Lyle	$b+1$	$b-4$
Sean	$c+1$	$c-4$

According to the equation,

  $\begin{array}{l}=b+1=2(c+1)\\ =b+1=2c+2\\ =b+1-2c-2=0\\ =b-2c-1=0\text{ (i)}\end{array}$

Also,

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

Substituting equation (ii) in (i)

  $\begin{array}{l}=b-2c-1=0\\ =(3c-8)-2c-1=0\\ =3c-8-2c-1=0\\ =c-9=0\\ =c=9\end{array}$

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

  $\begin{array}{l}=b=3c-8\\ =b=3(9)-8\\ =b=27-8\\ =b=19\end{array}$

Hence, the age of Sean is 9 years old now and age of Lyle is 19 years old now .

After a year , the age of Sean will be 10 years old and Lyle will be 20 years old.