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

Let the present age of father be x’

Let the age of daughter be ‘y’.

Before seven years, age of father is x – 7

Before seven years, age of daughter is y – 7.

Father was 7 times as old as daughter.

∴ x – 7 = 7 (y – 7)

x – 7 = 7y – 49

x – 7y = -49 + 7

x – 7y = – 42

∴ x – 7y + 42 = 0 …………….. (i)

After three years, age of father is x + 3

After three years, age of daughter is y + 3

Three years from now will three times as old as father.

∴ x + 3 = 3(y + 3)

x + 3 = 3y + 9

x – 3y + 3 – 9 = 0 

3 – 3y – 6 = 0 ………….. (ii) 

∴ Algebraically linear equations : 

x – 7y + 42 = 0 

x – 3y – 6 =0 

If we represent this linear equations through graph, we have 

(i) x – 7y + 42 = 0 

-7y = -x – 42 

7y = x + 42

∴ y = \(\frac{x + 42}{7}\)

x	0	7
y = \(\frac{x + 42}{7}\)	6	7

(ii) x – 3y – 6 = 0 

-3y = -x + 6 

3y = x – 6

∴  y = \(\frac{x - 6}{3}\)

x	0	+6
y = \(\frac{x - 6}{3}\)	-2	0