Name: marangeo
Who is asking: Other
Level of the question: All

Question: Hello!

I'd like your help please.

The following question and answer is posted on the website then Tease Your Mind and specifically the question dated 16 October 2003.

I recently lost my wallet and when it came to completing the police report I couldn't remember how much money I had in there. I do remember thinking that the first time I bought something that it cost me 10 per cent of what I had. Then I noticed that the second purchase had also cost me exactly 10 per cents of what I had left. My receipts totalled $19. How much did I have in my wallet when I lost it?

I believe the answer should be $81 for the following reason:

Since we are talking percentages, and my receipts
totalled 19 then my purchases cost me 19/100.

If my purchases cost 19/100 then I had 81/100 in my wallet when I lost it. Hence $81

Am I right or wrong?

Thanks for your help and time.


Hi Marangeo.

You are right. If we say that your initial amount was c, then you spent 10% of c on your first purchase and 10% of (90% of c) after your second purchase. Then you lost your wallet. You know that $19 in receipts equals this sum.

$19 = 10% c + 10% ( 90% c)

in decimal form:

19 = .1c + .1(.9c) = .1c + .09c = .19c
so c = 19/.19 = $100

This is the Initial amount before your purchase. The amount you had
when you lost your wallet was $100 - $19 = $81.

Stephen La Rocque.>