Question

Present age of father is 30 years more than twice that of his son. After 10 years, the age of father will be thrice the age of his son. Represent this situation algebraically and geometrically.

Answer 1

Let the present age of son = x year

and the age of his father = y year

According to the question

y = 2x + 30

or, 2x – y = – 30 …(1)

After 10 years,

Age of son = (x + 10)year

Age of father = (y + 10)year

So, According to the question

y + 10 = 3(x + 10)

y + 10 = 3x + 30

y = 3x + 20

or, 3x – y = – 20 …(2)

Now, table for y = 2x + 30

Now, table for y = 3x + 20

On plotting points on a graph paper and join them to get a straight line representing y = 2x + 30.

Similarly, on plotting the points on the same graph paper and join them to get a straight line representing y = 3x + 20.

Here, the lines representing Eq. (1) and Eq. (2) intersecting at point A i.e. (10,50).

So, the age of son is 10 years and age of his father is 50 years.