Question

Cary is 9 years older than dan in 10 years the sum of their ages will be 81 find the age of each now

Answer 1

Alright, lets get started.

Suppose Cary's current age = x

Suppose Dan's current age = y

Cary is 9 years older than Dan (given in question), means :

`x = y + 9` ...............................equation (1)

After 10 years Cary's age = (x+10)

After 10 years Dan's age = (y+10)

In 10 years the sum of their ages will be 81, means

`(x+10)+(y+10) = 81`

`x + y + 20 = 81`

Subtrating 20 in both sides

`x + y + 20 - 20 = 81- 20`

`x + y = 61` .................................... equation (2)

From equation (1), putting the value of x in equation (2)

`y + 9 + y = 61`

`2y + 9 = 61`

Subtrating 9 in both sides

`2 y + 9 - 9= 61 - 9`

`2 y = 52`

Dividing by 2 in both sides

`(2y)/(2) = (52)/(2)`

`y = 26`

`x = y + 9 = 26 + 9`

`x = 35`

It means Cary's age is 35 and Dan's age is 26. : Answer

Hope it will help :)