Question 1206119: Hi
Haresh gave 40% of his money and an additional $5 to Bob. He gave 75% of his remaining money and an additional $6 to Karen. The amount of money haresh had at the end was $44 less than what he gave to Karen. Find the amount haresh gave to Bob.
This is word for word from my sons textbook.
Found 6 solutions by Theo, math_tutor2020, Edwin McCravy, greenestamps, ikleyn, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your solution is as follows:
haresh originally had 115 dollars.
he gave 40% of that plus 5 dollars to bob = 51 dollars.
he had 115 - 51 = 64 dollars left.
he gave 75% of that plus 6 dollars to karen = .75 * 64 + 6 = 54 dollars.
he had 64 - 54 = 10 dollars left after he gave to karen.
10 dollars is 44 dollars less than 54 dollars which means he had 44 dollars less than what he gave to karen at the end.
your solution is that haaresh gave 51 dollars to bob.
my worksheet contains the details of the calculations.
let me know if you have any questions.
theo
Answer by math_tutor2020(3816)  (Show Source):
You can put this solution on YOUR website!
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 = 51 dollars 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 = 51 dollars 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
https://docs.google.com/spreadsheets/d/145sUDhOxWyWCcL4awl6FTGExxgmIxKLaN8802JNTDZQ/edit?usp=sharing
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: $51
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website!
Math tutor and I agree that the more unknowns you use for a word problem,
the easier they are to set up. Unfortunately, this musually make solving
them more difficult. So it's a give-and-take situation. I'll use 3 unknowns,
also.
Haresh had $H in the beginning.
He gave Bob $B.
He gave Karen $K
Haresh had $H
Haresh gave 40% of his money and an additional $5 to Bob.
Then Haresh gave Bob $B = 0.4H+5
So Haresh then had $(H-B)
He gave 75% of his remaining money and an additional $6 to Karen.
Haresh gave Karen $K = 0.75(H-B)+6
Haresh then had $(H-B-K)
The amount of money Haresh had at the end was $44 less than what he gave to Karen.
$(H-B-K) = K-44
Simplify and solve. See, that's 3 eq. in 3 unknowns.
But the set-up was easier.
H = $115, B = $51, K = $54
Find the amount Haresh gave to Bob.
He gave Bob $51.
Edwin
Answer by greenestamps(13196)  (Show Source):
Answer by ikleyn(52756)  (Show Source):
You can put this solution on YOUR website! .
Haresh gave 40% of his money and an additional $5 to Bob.
He gave 75% of his remaining money and an additional $6 to Karen.
The amount of money Haresh had at the end was $44 less than what he gave to Karen.
Find the amount Haresh gave to Bob.
~~~~~~~~~~~~~~~~~~~~~~
Let x be the Haresh's initial amount of money, in dollars.
After Haresh gave 40% of his money and an additional $5 to Bob, Haresh's remaining money
was (0.6x-5) dollars.
Then Haresh gave 0.75 of the remaining money and additional $6 to karen;
so Haresh gave to Karen 0.75*(0.6x-5) + 6 = 0.45x + 2.25 dollars.
After that, the amount of money Haresh had at the end was
(0.6x-5) - ((0.45x+2.25) = 0.15x - 7.25 dollars.
It is $44 less than 0.45x + 2.25; so we write this equation
0.15x - 7.25 = 0.45x + 2.25 - 44.
+-------------------------------------------+
| At this point, the setup is complete. |
+-------------------------------------------+
Now simplify the equation and find x
44 - 2.25 - 7.25 = 0.45x - 0.15x
34.5 = 0.3x
x =  = 115.
Thus Haresh had $115 initially.
Hence, the amount he gave to Bob was 0.4*115 + 5 = 51 dollar.
ANSWER. The amount Haresh gave to Bob was 51 dollar.
Solved using one unknown.
////////////////////
I am 179% sure that using one unknown
is the EXPECTED method for solving this problem.
Answer by MathTherapy(10549)  (Show Source):
You can put this solution on YOUR website!
Hi
Haresh gave 40% of his money and an additional $5 to Bob. He gave 75% of his remaining money and an additional $6 to Karen. The amount of money haresh had at the end was $44 less than what he gave to Karen. Find the amount haresh gave to Bob.
This is word for word from my sons textbook.
Let original amount Haresh had, be H
After giving Bob 40% of his money and an additional $5, Haresh had H - (.4H + 5) = .6H - 5, remaining
Amount Bob received from Haresh: .4H + 5
After giving Karen 75% of his remaining money and an additional $6, Haresh had:
.25(.6H - 5) - 6 = .15H - 1.25 - 6 = .15H - 7.25, remaining
Amount Karen received from Haresh: .75(.6H - 5) + 6 = .45H - 3.75 + 6 = .45H + 2.25
The amount of money Haresh had at the end was $44 less than what he gave to Karen, so we get:
.15H - 7.25 = .45H + 2.25 - 44
.15H - 7.25 = .45H - 41.75
.15H - .45H = - 41.75 + 7.25
- .3H = - 34.5
Original amount Haresh had, or 
Amount Bob received from Haresh: .4H + 5 = .4(115) + 5 = 46 + 5 = $51
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