Chapter 9.7, Problem 13P

To determine

To solve: the system of equations in two variables.

Answer to Problem 13P

The age of Steve is 12 years old now and age of Teresa is 4 years old.

Explanation of Solution

Given information:

Steve is three times as old as Theresa. In four years he will be twice as old as she will be.

Formula used:

Age problem.

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

Step2. Let b = the Steve’s age now.

Let c = the Theresa‘s age now.

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

Step4. Solve the equations.

Calculation:

Consider ,

Let b = the Steve’s age now.

Let c = the Theresa’s age now.

Age	Now	Four year
Steve	b	$b+4$
Theresa	C	$c+4$

According to the equation,

  $=b=3c\text{ (i)}$

Also,

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

Substituting equation (i) in (ii)

  $\begin{array}{l}=b-2c-4=0\\ =(3c)-2c-4=0\\ =3c-2c-4=0\\ =c-4=0\\ =c=4\end{array}$

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

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

Hence, the age of Steve is 12 years old now and age of Teresa is 4 years old .