Brain Teasers
A Day Out
Keith opened the door, hopped into the car and revved his engine. He was going to the small town exhibition.
He arrived at the exhibition not long after, and began wandering over to look at the different things.
At the gift shop he spent 50% of his overall money.
He then went on the Dodgems and spent 20% of the remaining money.
He entered a raffle which cost 50% of the remaining money.
He finally bought one hot dog which cost 10% of the remaining money.
He ended up with $22.50.
How much money did Keith start with, and how much did each thing cost?
He arrived at the exhibition not long after, and began wandering over to look at the different things.
At the gift shop he spent 50% of his overall money.
He then went on the Dodgems and spent 20% of the remaining money.
He entered a raffle which cost 50% of the remaining money.
He finally bought one hot dog which cost 10% of the remaining money.
He ended up with $22.50.
How much money did Keith start with, and how much did each thing cost?
Answer
You have to work backwards to get this right. All you know at this point is that Keith ended up with $22.50.The hot dog costs $2.50.
That would bring us up to $25.00. 10% of $25.00 equals $2.50 so if he spends $2.50 on the hot dog that brings us to $22.50, which is the starting point.
The raffle ticket was $25.00.
Before he buys the raffle ticket he has $50.00. He spends 50% of this, so then all you have to do is double $25.00 which makes $50.00.
The Dodgems were $12.50.
This means that before he went on the Dodgems he had $62.50. The Dodgems would have cost 20% of this, which is $12.50. That takes us to $50.00, which is where he was after the Dodgems.
The gifts cost $62.50.
Once again, you just have to multiply the money before the Dodgems by 2.
This means that he started with $125.
Hot Dog - $2.50
Raffle Ticket - $25.00
Dodgems - $12.50
Gifts - $62.50
Total - $125
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Comments
Good one!!!
Yay First one!!!
Yay First one!!!
Thanks, it's my first one
My first teaser that is
(((22.5/0.9)/0.5)/0./0.5=???
Damned emoticons... that should be an 8 followed by a )
great teaser, a little easy 4 me,JK
ya know over the summa i think i get a little dumber but once i got this right i was sooo happpy. ,HAHA great teaser anyway, enjoyed it a lot
ya know over the summa i think i get a little dumber but once i got this right i was sooo happpy. ,HAHA great teaser anyway, enjoyed it a lot
I keep getting $2.25 for the hot dog, how do you get $2.50, without knowing that the starting $ is $25.00? I did x (the amount he had before the hotdog) * .1 = $22.50 as my start. I know I'm doing something wrong, but I can't figure out how to solve it.
He had $25 before he bought the hotdog which cost 10% of that. 10% of $25 is $2.50 so that would have brought him down to $22.50.
I made it sort of doing a guess and check format, and seeing how close I was until I got it. There are probably definite ways to do it but I'm not a huge fan of the big mathematical formulas.
Youch! AWFUL explanation is not even an excuse for an answer! This exercise was not a brain teaser.
Instead of sloppy, circular reasoning do this:
Working backward, determine the percentage with which Keith was left. The hot dog purchase left him with 90% of his previous cash. $22.50 / .90 = $25.00. Which amount was 50% of his cash before buying raffle ticket. $25.00 / .50 = $50.00. Which is 80% of pre-Dodgems money. $50.00 / .80 = $62.50. This was 50% of the starting amount.
$62.50 / .50 = $125.00.
Instead of sloppy, circular reasoning do this:
Working backward, determine the percentage with which Keith was left. The hot dog purchase left him with 90% of his previous cash. $22.50 / .90 = $25.00. Which amount was 50% of his cash before buying raffle ticket. $25.00 / .50 = $50.00. Which is 80% of pre-Dodgems money. $50.00 / .80 = $62.50. This was 50% of the starting amount.
$62.50 / .50 = $125.00.
jae113 -
If you want to use x to solve, try this for the first one...
22.50 9
_____ = ___
X 10
then cross multiply...
you get 9x=225
divide both sides by 9
you get x=25
Good teaser, I loved the math, but convoluted answer...
If you want to use x to solve, try this for the first one...
22.50 9
_____ = ___
X 10
then cross multiply...
you get 9x=225
divide both sides by 9
you get x=25
Good teaser, I loved the math, but convoluted answer...
OK, that didn't work...
the 22.50 should be over the x and the 9 should be over the 10
the 22.50 should be over the x and the 9 should be over the 10
yeah I get the answer going from bottom to top..
but I tried in another way as well.. I know I'm wrong, could someone please make it clear what I exactly was it that I was doing wrong...
I took the starting amount to be x.. so the total money spent was x/2+x/10+x/20+x/200.. total money spent is also x-22.5... I equated these and the answer I get for x is wrong... where did I go wrong?
but I tried in another way as well.. I know I'm wrong, could someone please make it clear what I exactly was it that I was doing wrong...
I took the starting amount to be x.. so the total money spent was x/2+x/10+x/20+x/200.. total money spent is also x-22.5... I equated these and the answer I get for x is wrong... where did I go wrong?
You don't have to start at bottom. Start at top. Let M = initial amount
Remaining after Gift = 0.5M
Remaining after Dogem = 0.5M-(0.2x0.5M) = 0.4M
Remaining after Raffle = 0.2M
Remaining after hotdog = 0.2M-(0.1x.2M) = 0.18M
0.18M = $22.50
M=$22.50/0.18 = $125
Remaining after Gift = 0.5M
Remaining after Dogem = 0.5M-(0.2x0.5M) = 0.4M
Remaining after Raffle = 0.2M
Remaining after hotdog = 0.2M-(0.1x.2M) = 0.18M
0.18M = $22.50
M=$22.50/0.18 = $125
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