Question

Vandana's mother's age is 6 years more than twice Vandana's age. if the sum of their ages is 57 find their ages.

Answer 1

Let Vandana's Age =X
Vandana's Mother's Age = 6+2x
If the sum of their ages=57
A.T.Q
Vandana 17 and her mother 40 years

Answer 2

Let Vandanas's age be x.

Let Vandana's mother's age be y.

Vandana's mother's age is 6 years more than twice Vandana's age therefore:

y = 6+2x ; (eq 1)

By shifting:

y-2x = 6; (eq 2)

The sum of their ages is 57 therefore:

y+x = 57; (eq 3)

Take LCM of both equations:

1(y-2x=6) = y-2x=6 (eq4)

2(y+x=57) = 2y+2x=114 (eq 5)

By adding eq 4 to 5:

+y-2x = 6

+2y+2x=114

+3y = 120  

y = 120/3

y=40

Put y in eq 3

y+x = 57

40+x = 57

x = 57-40

x = 17

So Vandana's mother's age is 40 and Vandana's age is 17.