SOLUTION: Mary is twice as old as John was 3 years ago. In 5 years John will be 1 year older than Mary is now. Find the ages of both people today.

Question 585418: Mary is twice as old as John was 3 years ago. In 5 years John will be 1 year older than Mary is now. Find the ages of both people today.
Answer by Schaman_Dempster(26) (Show Source): You can put this solution on YOUR website!
Let the ages of Mary and John be x and y years respectively today.
3 years ago, age of John was (y-3) years
Since Mary is twice as old as john was 3 years ago.
So, x = 2(y-3)
or x = 2y - 6 -------- (1)
In 5 years, age of John will be = (y + 5) years
"John will be 1 year older than Mary is now"
So, (y+5) = x + 1
or x = y + 5 -1
or x = y + 4 --------(2)
Using equation (1) and (2), we get:
2y - 6 = y + 4
2y = y + 4 + 6
2y = y + 10
y = 10

Plugging back the value of y in equation (2)
x = 10 + 4
x = 14

Hence, Age of Mary today is x= 14 years and age of John today is y=10 years.
Hope this helps~!

RELATED QUESTIONS
Mary is 3 times as old as her brother John. In 5 years, Mary will be twice as old as... (answered by richwmiller)

Mary is fourteen years older than John, and next year she will be twice as old as John.... (answered by lwsshak3)

Fred is 5 years older than Mary. In 4 years, Fred will be twice as old as Mary was one... (answered by Alan3354)

at the moment john is 5 years older than mary. in seven years mary age will be 3/4 of... (answered by lwsshak3)

5 years ago, Jay was seven years older than Mary. In five years, Mary will be half as old (answered by bluemockingjay7)

Mary is 21 years older than john in 12 years time Mary will be twice as old as John what... (answered by Maths68)

The sum of the ages of John and Mary is 32. Four years ago, John was twice as old as... (answered by josgarithmetic,ikleyn)

Mary is 3 years older than her brother Tom, and Tom is 4 years older than John. Three... (answered by drj)

Mary is 3 years older than her brother Tom, and Tom is 4 years older than John. Three... (answered by Maths68)