SOLUTION: A DOUBLE BIRTHDAY: "Your birthday today and also your son's! That's amazing. How old is he now?" Bob smiled. "I'll tell you with fractions. One over his age, plus one over my

Question 144721: A DOUBLE BIRTHDAY:
"Your birthday today and also your son's! That's amazing. How old is he now?"
Bob smiled. "I'll tell you with fractions. One over his age, plus one over my age, makes one over seven. That's one-seventh, of course."
So what were their respective ages?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The given relationship, if the son's age is and the father's age is , is .

Solving for y we get:

We also know that since today is their mutual birthday, their ages must be integers.

We also know that the father's age cannot be a negative number and we cannot divide by zero, therefore the son's age must be an integer greater than or equal to 8.

Let's try 8: . 56 is an integer, so age 8 for the son, and 56 for the father is a solution. But are there any others?

Let's try 9: . Not an integer AND smaller than 56

Let's try 10: . Not an integer and smaller than

Ah hah! As the son's possible age increases, the father's possible age decreases. This suggests an upper limit to the son's age -- after all, the father must be older than his son (discounting any weird genetic engineering or travel near the speed of light scenarios).

Let's try 14: . An integer, but impossible because both the father and son could not have been born on the same day.

You can check out 11, 12, and 13 as potential ages for the son.

RELATED QUESTIONS
Today your son is 12 years old. Your son will also begin college on his 18th birthday.... (answered by Theo)

Two Russian mathematicians meet on a plane. �If I remember correctly, you have three (answered by ankor@dixie-net.com)

Today is bobs birthday. In 50 years time bob will be three times as old as he will be in... (answered by TimothyLamb)

You have just turned 12 years old. Your mother promises to give you a car worth $15,000... (answered by ankor@dixie-net.com)

Today is Teresa�s birthday. She is 6 years old. How old is Teresa in months? (answered by Alan3354)

Each year on Colin�s birthday (since his first birthday), he celebrates with a birthday... (answered by richwmiller)

My son asked me this on his birthday, yesterday: His birthday is 31st August, and he... (answered by Theo)

On your fifteenth birthday, you received $1,000 which you invested at 10.3 percent... (answered by solver91311)

``Two Russian mathematicians meet on a plane. �If I remember correctly, you have... (answered by Edwin McCravy,the_answer_man)