Question

The mean of the ages of father and his son is 27 years. After
18 years, father will be twice as old as his son. Their present ages a

Answer 1

Answer:

The son is 12 years old, and the father is 42.

Step-by-step explanation:

x = the father’s current age

y = the son’s current age

If the mean is 27, then the combined age is 54.

x + y = 54

x + 18 = 2 (y + 18)

x + 18 = 2y + 36

Subtract (2y + 18) from both sides

x - 2y = 18

So now we have 2 important equations:

x - 2y = 18, and

x + y = 54.

There are two ways to solve this. You can eliminate the y or the x.

Eliminating y:

(x + y = 54) * 2

2x + 2y = 108

x - 2y = 18

When the equations are added together, the y cancels out, leaving you with

3x = 126

x = 42

42 + y = 54

y = 12

Eliminating x:

x - 2y = 18

When the signs of each term in this equation are reversed, you get

-x + 2y = -18

Add the (x + y = 54) to get

3y = 54 - 18

3y = 36

y = 12

x + 12 = 54

x = 42