Question 1206119
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A = amount Haresh starts with
B = amount Haresh has leftover after giving some amount to Bob (before giving anything to Karen)
C = amount Haresh has leftover after giving some amount to Karen (and Bob previously)


In other words, Haresh will have bank balances of A,B, and C in that order after giving to Bob first and then Karen next.


0.4A+5 = amount given to Bob
B = A - (0.4A+5) 
B = A - 0.4A - 5
B = 0.6A - 5


0.75B + 6 = amount given to Karen
C = B - (0.75B+6)
C = B - 0.75B - 6
C = 0.25B - 6


C = (amount given to Karen) - 44
C = (0.75B + 6) - 44
C = 0.75B - 38


We determine that
C = 0.25B - 6
and
C = 0.75B - 38


Equate the right hand sides so we can determine B.
0.75B - 38 = 0.25B - 6
0.75B - 0.25B = -6 + 38
0.50B = 32
B = 32/0.50
B = 64
Haresh will have $64 after giving some amount to Bob, but this is before Haresh gives any money to Karen.


Use this value of B to find A.
B = 0.6A - 5
64 = 0.6A - 5
64+5 = 0.6A
69 = 0.6A
A = 69/0.6
A = 115
Haresh started with $115.


Let's use the value of B to find C.
C = 0.25B - 6
C = 0.25*64 - 6
C = 16 - 6
C = 10
Haresh ends up with $10 after giving some amounts to Bob and Karen.
Or we can compute it like this:
C = 0.75B - 38
C = 0.75*64 - 38
C = 48 - 38
C = 10
Or like this:
C = 0.15A - 7.25
C = 0.15*115 - 7.25
C = 17.25 - 7.25
C = 10
You only need to use one equation to find C, but it helps to check multiple equations to ensure we get the same result each time.


To summarize,
A = 115 = amount Haresh started with
B = 64 = amount Haresh has left after he gives some money to Bob (before Karen gets any money)
C = 10 = amount Haresh has left after giving some money to Karen (Bob already got his gift)


The gap from A to B is A-B = 115-64 = <font color=red>51 dollars</font> which is the amount Haresh gave to Bob.
Note 40% of 115 = 0.40*115 = 46 dollars is given to Bob and then another extra $5, so that's 46+5 = <font color=red>51 dollars</font> total given to Bob.


The gap from B to C is B-C = 64-10 = 54 dollars which is the amount given to Karen.
75% of what Haresh has left (the $64) is 0.75*64 = 48 dollars is given to Karen, in addition to another extra $6. So she gets 48+6 = 54 dollars.
Haresh ultimately ends up with 64 - 54 = 10 dollars.
Notice $10 is $44 less than what he gave to Karen (she got $54).
This helps us verify the solution is correct.


Another way to confirm the answer is to use a spreadsheet as shown here
<a href="https://docs.google.com/spreadsheets/d/145sUDhOxWyWCcL4awl6FTGExxgmIxKLaN8802JNTDZQ/edit?usp=sharing">https://docs.google.com/spreadsheets/d/145sUDhOxWyWCcL4awl6FTGExxgmIxKLaN8802JNTDZQ/edit?usp=sharing</a>
You do not need a Google account to access this spreadsheet. 
Click any cell to see what formula I used for it. The formula bar is at the top.



Answer: <font color=red size=4>$51</font>
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