Math problem about age

by Sahana
(Kolkata)

Arvind is eight years older than his sister. In three years, he will be twice as old as his sister. how old are they are now?

Solution

Let x be a Arvind's age.

Let x - 8 be his sister's age.

In 3 years, Arvind's age will be x + 3

In 3 years, the sister's age will be x - 8 + 3 = x - 5

In 3 years, Arvind is twice as old as his sister.

x + 3 = 2 × (x - 5)

x + 3 = 2x - 10

2x - 10 = x + 3

Subtract x from both sides.

2x - x - 10 = x - x + 3

2x - x - 10 = 3

Add 10 to both sides

2x - x - 10 + 10 = 3 + 10

2x - x = 3 + 10

x = 13


Arvind's age is 13

His sister's age is 13 - 8 = 5.

In 3 years, Arvind's will be 16 and the sister will be 8.

16 is twice as big as 8.