Where is the missing number?

Can anyone help me answer this?..

You see a shirt for £97, but you don't have any money.

You borrow £50 from your mum, and £50 from your dad, so you have £100.

You buy the shirt, and have £3 change.

So you give your mum £1, your dad £1 and keep the other £1.

You now owe your mum £49 and your dad £49.

£49 + £49 = £98 and your £1 makes £99.

Where is the missing £1?

Re: Where is the missing number?

Quote:

Originally Posted by

**benjiman46** Where is the missing £1?

You owe 49 pounds to your dad and 49 to your mum. You have 1 pound so, you need __another pound__ to payng your debt.

Re: Where is the missing number?

Think of it this way:

Your debt is 100 pounds combined. After giving back 1 pound to your mom and 1 pound to 1 dad **reduces** your debt by 2. So now your debt is 98 pounds. That means that any number of pounds you have with you can only be used to reduce the debt, and not to increase it. In terms of mathematical operations, the number of pounds you have with you can only be subtracted from the total debt, not added to the debt. The one pound you are left with can only be used to reduce your debt by one, meaning it cannot be added to 98 to get the result 99, but only subtracted from 98 to get the correct answer 97. Get it?

Nothing is missing, you are just forced into paradox by the incorrect operation performed between the debt of 98 pounds and the one pound you have with you.

I hope nothing is lost in translation since English is not my native language.

Re: Where is the missing number?

Quote:

Originally Posted by

**FernandoRevilla** You owe 49 pounds to your dad and 49 to your mum. You have 1 pound so, you need __another pound__ to payng your debt.

Oh professor, you should know better than that! ;)

Re: Where is the missing number?

Quote:

Originally Posted by

**MathoMan** Oh professor, you should know better than that! ;)

I didn't explain it well. Your correct approach is about the coherence of the shirt's price, and mine one about the coherence of the debt. In your case $\displaystyle 49+49-1=97$, in my case $\displaystyle 100=1+1+(98-1)+1(\mbox{the pound the son has})$.

Re: Where is the missing number?

No hard feelings professor, I was just teasing you a bit. Math on!

Re: Where is the missing number?

Quote:

Originally Posted by

**MathoMan** No hard feelings professor, I was just teasing you a bit. Math on!

No problem, I am very fond of irony (although *provisionally* retired, I must confess).

Re: Where is the missing number?

Solution: anyone who pays £97 for a single shirt is obviously crazy. Therefore the "missing £1" is the result of a psychotic episode!

Re: Where is the missing number?

Quote:

Originally Posted by

**HallsofIvy** Solution: anyone who pays £97 for a single shirt is obviously crazy. Therefore the "missing £1" is the result of a psychotic episode!

Yep, but that solution is the trivial one. :D