# Tanya turns 5

This was the fifth birthday of Tanya. Her grandpa, Mister John Smith, decided to have a big celebration. All birthdays of Tanya were celebrated but this was the first time she was asked which friends she wanted to invite.

Many people came for Tanya’s birthday party. There were the neighbours, the friends of her grandpa, grandma, papa and mom. Also there were the guests Tanya has asked for: Tinku, Peter and Kate. These kids were her own age and she played with them all the time. Most importantly, Tanya’s uncle had also come. Tanya really loved him. He lived in Toronto and had come all the way for Tanya’s birthday.

# Birthday presents

Everyone gave presents to Tanya. They gave her dolls, cars, other toys and even some items of clothing. The present she loved the most was from her uncle. It was a baby blue colored backpack on which rhinestones spelled TANYA in large letters.

Grandpa came to tell Tanya a bedtime story. Tanya told him that, instead of a story, she wanted to ask some questions. Grandpa was surprised but agreed.

# How old is everyone?

Tanya: Grandpa, I want to ask you the age of everyone in the family. How old is my mother?

Grandpa: Tanya, your mother was 30 years old on her last birthday.

Tanya: Because I am 5 years old, To subtract 5 from 30, I will count 5 times backwards 30, 29, 28, 27,26. That means my mother is 25 years older than I am. What about my papa?

Grandpa: Your papa was 5 years older than your mom when they got married. So, I guess he must still be 5 years older than her.

Tanya: That is funny. He will always be 5 years older than mom. That means he is 30 plus 5 which 35 years old, right?

Grandpa knew the next question and said: Your uncle is 7 years younger than your papa.

# When will I have an aunt?

Tanya counted backwards from 35 on her fingers and then said: Grandpa 35 minus 7 is 28. So uncle is only 28 years old. My mom is 30. 28 plus 2 is 30. So he is even younger than my mom by 2 years.

**When will I have an aunt?**

Grandpa: I don’t know when. Why don’t you ask uncle? I guess you also want to know how old I am. Do you want to guess?

Tanya: Let me guess, my papa is 30 years older than I am. He is 35 years old. Three plus three is six, and 30 plus 30 will be 60. So, 30 plus 35 must be 65. Are you 65 years old?

Grandpa: Good guess. It is very close. I am 63 years old. Now you guess your grandma’s age.

Tanya: My mom is 5 years younger than my papa. So if grandma is 5 years younger than you, she is (counting backwards 62, 61, 60, 59, 58) 58 years old.

Grandpa: Good guess but she is only 57 years old. I am 6 years older than her. Tanya, this better be your last question. You have to sleep so that you can wake up in time for school tomorrow. So what is your last question?

# Will I have to marry someone older?

Tanya: Grandma married someone 6 years older than her, mom married someone 5 years older than her. Will I also have to marry someone older than me? Do you think I would not be able to marry Tinku because he is about the same age as I am.

Grandpa: Where do you get this dream about your marriage? You are only 5 years old. Now, you better go to sleep.

Then Grandpa gave a good night hug and a kiss to Tanya, and tucked her in bed. We don’t know if Tanya dreamed that night about her marriage or not. She did not mention it.

*Challenge*

Find the ages of as many relative as you can. Determine who is older than whom and by how many years?

*No solution given for the challenge because the answer is different for each person*.

### Supplementary

John and Jane have four children Dee, Ron, Kate and Lily. John and Jane got married 10 years ago. Dee was born 3 years after the marriage, Ron 4 years after the marriage, Kate 6 years after the marriage and Lily 8 years after the marriage. How old are the children?

There are two ways to do this. Let us figure out Dee’s age. Her age plus 3 years will be 10. That means Dee is 7 years old because 7 + 3 = 10. Ron was born 4 years after the marriage and Dee 3 years after the marriage. Ron is then one year younger than Dee or 6 years old, Kate is 6 – 4 or 2 years younger than Ron or 4 years old. Lily was born even two years later. So she must be 2 years old.

Another way to do is: Dee is 10 – 3 = 7. Ron is 10 – 4 = 6, Kate is 10 -6 = 4 and Lily is 10 – 8 = 2 years old.

A visual way of doing this is to write the numbers from 1 to 10 to show the number of years the kid was born after marriage. The next number is their age.

1 2 3 4 5 6 7 8 9 10 Dee

1 2 3 4 5 6 7 8 9 10 Ron

1 2 3 4 5 6 7 8 9 10 Kate

1 2 3 4 5 6 7 8 9 10 Lily

We get the same answer. It is good to check your answers this way.