# Blog

## Curious times

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Maryam had been practising the times tables really hard, so she was on the alert for interesting patterns. On her dad’s birthday she noticed something special.

“You’re four times older than me, Dad,” she exclaimed.

Four years later, she was counting the candles on her Dad’s birthday cake when she realised something mathematical.

“You’re three times older than me,” she noted.

How old is Maryam’s dad now?

Maryam’s dad used to be four times her age, so why isn’t that true now?

Imagine she’d said, “You’re four times older than me, Dad,” again. She’d be wrong, but we need to look at why.

Maryam is four years older than she was. If we multiply her current age by four, we get her old age times four, plus four times four. That’s 16 more than it used to be, whereas her dad is only four years older.

Four times Maryam’s current age is older than her dad. It’s older by 16 – 4 = 12 years.

To finish the question, we need to look at Maryam’s second statement. Three times her current age is exactly equal to her dad’s age.

That means Maryam is 12 years old!

If Maryam is 12, and her dad is three times older than she is, her dad must be 36.

Can you think of any other ways to solve the problem? Post them in the comments below!

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## 7 responses

1. Martin Towell

We can look at it algebraically. Let’s use M and D for Maryam and Dad, respectively.

The first statement can be written as
-> D = 4 M

The second statement can be written as
-> D+4 = 3 (M+4)

Let’s expand and simplify the second equation
-> D+4 = 3 M + 12 [expand the brackets]
-> D = 3 M + 8 [subtract 4 from both sides]

We now have two equations where “D = something”, so the two somethings must equal each other.
-> 4 M = 3 M + 8
-> M = 8 [subtract 3 M from both sides]
Therefore
-> D = 4 M = 4 x 8 = 32

When it is “four years later”
-> OlderM = M + 4 = 8 + 4 = 12
-> OlderD = 3 M = 3 x 12 = 36

2. Anna Alpass

I did it the same was as Martin.
Simultaneous equations are one thing from high school math that do actually come in handy!

3. Kylie

I used Martin’s method too 🙂

4. BunnyGirl

Same 🙂

Yep, after we talked about some ‘trial and error’ examples together, I pulled out the algebra …old school parent style 🙂
And reading the text solution example didn’t make that way any easier for me, showing my age too maybe?
Now, where’s my foot cream, I need my foot cream.

6. Jack

I think you are all forgetting something. This is that four times older means five times as old, and three times older means four times as old. This is simple linguistics, and in an English problem solving question, must be followed. If we proceed to answer this question with the correct English semantics in mind, then we will get an answer of Maryan being 12, and her dad being 60, four years ago, and Maryan becoming 16, while her dad 64 four years after that.

1. David

You make an interesting point Jack!

As an editor, and mathematician, I’m really intrigued by the implications of what you’re saying. I guess you’re implying that ‘older’ is a strictly additive comparison? I mean, multiplication by a number greater than 1 also implies an increase. But you’re probably right, a prescriptivist reading would give your answer.

A descriptivist reading would rely on other people’s interpretations – we have five examples in the comments that all agree D = 4 M. So that’s common usage, and they’re right, no matter what a deeper grammatical analysis says. There’s some weight to this account too – I don’t think anyone would ever say ‘one times older’ if they meant ‘twice as old’.

I’ll try to be clearer in future, and steer away from saying ‘times older’ rather than ‘as old’.

Thanks for the mid-afternoon brain-burner!

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