Chapter 9.7, Problem 27P

To determine

To solve: the system of equations in two variables.

Answer to Problem 27P

The age of father is 36 years old now and age of son is 10 years old now .

Explanation of Solution

Given information:

A father, being asked his age and that of his son , said ,”If you add 4 to my age and divide the sum by 4, you will have my son’s age. But 6 years ago I was $7\frac{1}{2}$ times as old as my son. ”

Formula used:

Age problem.

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

Step2. Let b = the father’s age .

Let c = the son‘s age .

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

Step4. Solve the equations.

Calculation:

Consider ,

Let b = the father’s age now .

Let c = the son’s age now .

According to the question,

  $=\frac{4+b}{4}=c\text{ (i)}$

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

Age	Six year ago
Father	$b-6$
Son	$c-6$

This implies $(b-6)=7\frac{1}{2}(c-6)$

  $\begin{array}{l}=b-6=\frac{15}{2}(c-6)\\ =b-6=7.5(c-6)\\ =b-6=7.5c-45\\ =b-7.5c=-45+6\\ =b-7.5c=-39\text{ (iii)}\end{array}$

Substituting equation (ii) in (iii) we get,

  $\begin{array}{l}=4c-4-7.5c=-39\\ =-3.5c-4=-39\\ =-3.5c=-39+4\\ =-3.5c=-35\\ =\frac{3.5c}{3.5}=\frac{35}{3.5}\\ =c=10\end{array}$

Putting value of c in equation (ii)

  $\begin{array}{l}=b=4(10)-4\\ =b=40-4\\ =b=36\end{array}$

Hence, the age of father is 36 years old now and age of son is 10 years old now .