Expert: Ahmed Salami - 4/20/2010

Question
The sum of the ages of Mary and Harry is 40 years. In 7 years, Mary will be twice as old as Harry. How old is Mary now?

Answer
Hi Braydon,
Let Mary's age be x and Harry's be y. At present,
x + y = 40
x = 40 - y
In 7 years, their ages are now x+7 and y+7.
So, we have
x + 7 = 2(y + 7)
x + 7 = 2y + 14
x = 2y + 14 - 7
x = 2y + 7
Equating the expressions for x in both cases,
40 - y = 2y + 7
collecting like trms,
40 - 7 = 2y + y
33 = 3y
y = 33/3
 = 11
x = 40 - y
 = 40 - 11
 = 29

Mary is 29 years old now.

Regards