**Question 1. 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.**

**Solution:**

Let

age of Aftab is represented by x

age of daughter is represented by y

Then** **Seven years ago,

age of Aftab = x -7

age of daughter = y-7

given that I was seven times as old as you were so we get

x - 7 = 7 ( y – 7 )

x – 7 = 7 y – 49

x- 7 y = - 49 + 7

x – 7 y = - 42 …(1)

x = 7 y – 42

plug y = 5,6 and 7 we get

x = 7 * 5 - 42 = 35 - 42 = - 7

x = 7 * 6 - 42 = 42 – 42 =0

x = 7 * 7 – 42 = 49 – 42 = 7

three years from now ,

Age of Aftab = x +3

Age of daughter = y+3

Given that I shall be three times as old as you will be so we get

x + 3 = 3 (y + 3)

x + 3 = 3 y + 9

x -3 y = 9- 3

x -3 y = 6 …(2)

x = 3 y + 6

plug y = -2,-1and 0 we get

x = 3 * - 2 + 6 = -6+6 =0

x = 3 * - 1 + 6 = -3+ 6 = 3

x = 3 * 0 + 6 = 0 + 6 = 6

**Algebraic representation **

**From equation (1) and (2)**

x – 7 y = – 42 …(1)

x - 3 y = 6 …(2)

**Graphical representation **

** **** **