A lady has a certain number of dollar bills in her purse. She has no other money. She spends half the money on a hat and gives $1 to a begger outside the store.She spends half the remaining dollars for lunch and tips the waiter $2. She then spends haif the remaining dollars for a book, and just before she goes home she spends $3 dollars on a hot fudge sundae. She now has $1 left. How many dollars did she began with?
$42
Thanks Ali.What did you do?
Let the original amount be $x
Amount left after first episode
= x/2 - 1
amount left after lunch
= (x/2-1)/2 - 2
amount left after buying book
= [(x/2-1)/2 - 2]/2
amount left after buying fudge
= [(x/2-1)/2 - 2]/2 - 3
then[(x/2-1)/2 - 2]/2 - 3 = 1
[(x/2-1)/2 - 2]/2 = 4
[(x/2-1)/2 - 2] = 8
(x/2-1)/2 = 10
x/2 - 1 = 20
x/2 = 21
x = 42
$6.00
42/2=21
21-1=20
20/2=10
10-2=8
8/2=4
4-3=1
the answer is $42
To find out how many dollars the lady began with, we can work backwards by undoing each step.
Let's start with the final amount of $1 left.
1. Before spending $3 on a hot fudge sundae, she had $1 left. So, after buying the sundae, she had $1 + $3 = $4 remaining.
2. She spent half of the remaining dollars on a book. So, before buying the book, she had $4 x 2 = $8 remaining.
3. Just before buying the book, she spent $2 on tipping the waiter. So, before tipping, she had $8 + $2 = $10 remaining.
4. Again, she spent half of the remaining dollars for lunch. So, before lunch, she had $10 x 2 = $20 remaining.
5. Before lunch, she gave $1 to a beggar outside the store. So, before giving to the beggar, she had $20 + $1 = $21.
6. Lastly, she spent half of the money on a hat. So, before buying the hat, she had $21 x 2 = $42.
Therefore, the lady initially had $42 in her purse.