not getting it

S

sujoy

Junior Member
Joined
Apr 30, 2005
Messages
110
Sir here is the problem :
Alex had some money on monday morning.Everyday Alex half of the money he
has at the beginning of the day on food & donated $200 out of the
remaining to a philanthropic organisation. On saturday evening after his
spending& donation , he was left with $25.
How much money did Alex spend on Wednesday on food?

ans---3200(most likely)
thanks,
regards,& respect
sujoy
 
Saturday (day 0) he spent $425 total. Each day (going backwards) he spent twice as much so on day N he spent
425*2^N - 200 on food.
Wedensday was day 3 so he spent 3200 as you said.
Incidently at the end of day N he had 25+425*((2^N)-1) dollars. Monday he started with 26,800. Big appetite.
 
Respected Sir(Gene)
THANK YOU VERY VERY MUCH
SIR I have a doubt;
How do you know in saturday he spent 425 in total
basically I am a bit confused with this problem
with RESPECT & YOUR BLESSINGS
Sujoy
 
He ended up with $25.
He had $x in the morning.
He spent $200 on charity.
He spent x/2 on food.
x-x/2 - 200 = 25
x/2 = 225
x = 450
Checking:
He started Saturday with 450
He spent 450/2 + 200 = 425
He had 25 at the end of the day.
It works.
 
Hello, sujoy!

Gene had the best and cleverest solution.

Alex had some money on Monday morning.
Everyday Alex half of the money he has at the beginning of the day on food
and donated $200 out of the remaining to a philanthropic organisation.
On Saturday evening after his spending & donation , he was left with $25.

How much money did Alex spend on Wednesday on food?

Ans: 3200 (most likely) . . . correct! How did you get it?
Click to expand...
We can "walk" through this problem . . . but it's very very long and tedious.

On Monday morning, Alex had X dollars.
. . He spent half of it, X/2, and had the other half left, X/2.
. . Then he gave away $200.
. . He had: .X/2 - 200 .dollars left.

On Tuesday, he spent half his money: .(X/2 - 200)/2
. . and had the other half left: .X/4 - 100
. . Then he gave away $200.
. . He had: .X/4 - 100 - 200 .= . X/4 - 300 .dollars left.

On Wednesday, he spent half his money: .(X/4 - 300)/2
. . and had the other half left: X/8 - 150
. . Then he gave away $200.
. . He had: .X/8 - 150 - 200 .= .X/8 - 350 .dollars left.

On Thursday, he spent half his money: .(X/8 - 350)/2
. . and had the other half left: .X/16 - 175
. . Then he gave away $200.
. . He had: .X/16 - 175 - 200 .= .X/16 - 375 .dollars left.

On Friday, he spent half his money: .(X/16 - 375)/2
. . and had the other half left: .X/32 - 187.5
. . Then he gave away $200.
. . He had: .X/32 - 187.5 - 200 .= .X/32 - 387.5 .dollars left.

On Saturday, he spend half his money: .(X/32 - 387.5)/2
. . and had the other half left: . X/64 - 193.75
. . Then he gave away $200.
. . He had: .X/64 - 193.75 - 200 .= .X/64 - 393.75 .dollars left.

And we're told that this amount is equal to $25.

There is our equation: . X/64 - 393.75 . = . 25

Solve for X: . X .= .$26,800 . (Alex's intial amount of money)

Therefore, on Wednesday, he spent:
. . . X/8 - 150 . = . 26800/8 - 150 . = . $3200

[I <u>told</u> you it was long!]
 
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