Ages

[abclindia]

after three years sam's teacher will be six times older than Sam was last year.the sum of Sam and his teacher's current age is 68.What will be their ages after five years?

[mac44]

Sam 16, teacher 62.

[Ellipsis]

Full working ...

Let Sam's current age be x and his teacher's be y

> after three years sam's teacher will be six times older than Sam was last year

This gives us

6(x-1) = y+3

> the sum of Sam and his teacher's current age is 68

This gives us

x+y = 68

We therefore have simultaneous equations to solve:

1) 6(x-1) = y+3
2) x+y = 68

From 1):

3) 6x - 6 = y + 3

From 2):

4) x = 68 - y

Add 3) and 4):

6x - 6 + x = y + 3 + 68 - y
7x -6 = 71
7x = 77
Therefore
5) x = 11

Substitute 5) back into 2):
11+y = 68
Therefore
6) y = 57

Check x and y in 1):
6(11-1) = 57+3
6 x 10 = 70 correct

Therefore the current ages are 11 and 57

> What will be their ages after five years?

16 and 62

[Ellipsis]

Sorry, typo, should read

6 x 10 = 60 correct