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?
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!]