Question

Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Answer 1

Step 1: Let's find the age of Aftab and his daughter :

Let the current age of Aftab be ‘$x$’.

And, the current age of his daughter be ‘$y$’.

Now, we can write, seven years ago,

Age of Aftab = $x-7$

Age of his daughter = $y-7$

According to the given condition

$\begin{array}{rcl}x-7& =& 7\left(y-7\right)\\ x-7& =& 7y-49\\ x-7y& =& -42\to \left(1\right)\end{array}$

Also, three years from now or after three years,

Age of Aftab will become = $x+3$

Age of his daughter will become = $y+3$

According to the situation given,

$$\begin{gathered} \left(x+3\right)=3(y+3) \\ \Rightarrow x+3=3y+9 \\ \Rightarrow x-3y=6\to \left(2\right) \end{gathered}$$

Subtracting equation (i) from equation (ii) we get

$\begin{array}{rcl}(x-3y)-(x-7y)& =& 6-(-42)\\ & \Rightarrow & -3y+7=6+42\\ & \Rightarrow & 4y=48\\ & \Rightarrow & y=12\end{array}$

The algebraic equation can be solved as

$$\begin{gathered} x-7y=-42 \\ x-3y=6 \end{gathered}$$

For, $x-7y=42\mathrm{or}x=-42+7y$

Step 2: Representing the scenario algebraically.

The solution table is

x	-7	0	7
y	5	6	7

For, $x-3y=6\mathrm{or}\mathrm{x}=6+3\mathrm{y}$

The solution table is

x	6	4	0
y	0	-1	-2

Step 3: Representing the scenario graphically.

Hence, the answer.