A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money did Bob receive?
A) 20
B) 22
C) 24
D) 26
E) 52
Tough word problem - dividing $
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A) 4 + (x-4)/2
B) 4 + 1/3 [(X-12)/2]
C) 2/3 [(X-12)/2] = 32 ; (x-12) = 3 x 32
SO 4 + 1/3 [(X-12)/2] = 4+ 1/3 ( 3x32/2) = 20
B) 4 + 1/3 [(X-12)/2]
C) 2/3 [(X-12)/2] = 32 ; (x-12) = 3 x 32
SO 4 + 1/3 [(X-12)/2] = 4+ 1/3 ( 3x32/2) = 20
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- logitech
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So they had 108 dollars total
A ) 4 + 104/2 = 4+ 52 ( 52 remained )
B ) 4 + 1/3 ( 48 ) = 20 ( 32 remained )
C) 32
A ) 4 + 104/2 = 4+ 52 ( 52 remained )
B ) 4 + 1/3 ( 48 ) = 20 ( 32 remained )
C) 32
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"DON'T LET ANYONE STEAL YOUR DREAM!"
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"DON'T LET ANYONE STEAL YOUR DREAM!"
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Nice work, Logitech
My solution is below. Note that we don’t need to consider Ann’s portion in the solution. We can just let K be the money remaining after Ann has received her portion and go from there.
Our equation will use the fact that, once we remove Bob’s portion, we have $32 for Chloe.
So, we get K – Bob’s $ = 32
The equation is K-4 – (K-4)/3 = 32
Solve for K (K=52) and then determine Bob’s portion ($20).
The answer is, indeed, A
My solution is below. Note that we don’t need to consider Ann’s portion in the solution. We can just let K be the money remaining after Ann has received her portion and go from there.
Our equation will use the fact that, once we remove Bob’s portion, we have $32 for Chloe.
So, we get K – Bob’s $ = 32
The equation is K-4 – (K-4)/3 = 32
Solve for K (K=52) and then determine Bob’s portion ($20).
The answer is, indeed, A
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that's BRILLIANT!kamu wrote:Bob took $4 + 1/3 of leftover..
that implies 2/3rds is left for Chloe..
if 2/3 of leftover = $32
1/3 of leftover = $16
$16+$4 = $20.
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One of the rules that I had read was that normally there is no 'useless' information that is provided, so in case you can solve a sum without using all the inforamation then you must be wrong.Brent Hanneson wrote:Nice work, Logitech
My solution is below. Note that we don�t need to consider Ann�s portion in the solution. We can just let K be the money remaining after Ann has received her portion and go from there.
Our equation will use the fact that, once we remove Bob�s portion, we have $32 for Chloe.
So, we get K � Bob�s $ = 32
The equation is K-4 � (K-4)/3 = 32
Solve for K (K=52) and then determine Bob�s portion ($20).
The answer is, indeed, A
How does one know that all the complicated information in this sum is not to be used??
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Hell All ,
The method that I am mentioning is quite long , but I want to know where I went wrong .
A - > 4 + (n-4) /2 - > (n+4)/2
B -> 4+ 1/3(n- (n+4)/2 -> (28+n)/6
C ->32
Hence , on solving this I get the total amount to be 116
Followed by Bob's share to be 24.
The method that I am mentioning is quite long , but I want to know where I went wrong .
A - > 4 + (n-4) /2 - > (n+4)/2
B -> 4+ 1/3(n- (n+4)/2 -> (28+n)/6
C ->32
Hence , on solving this I get the total amount to be 116
Followed by Bob's share to be 24.
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Good way of thinking about it, even shorter than the way I did it. I thought of it as Anne taking 1/2, Bob took 1/3 of leftover, which is 1/3x1/2=1/6, so Chloe is left with 1/3 of total - 8 dollars. Since 1/3=32, Total =96. Plug back into equation for Bob = 1/6*96 + 4.kamu wrote:Bob took $4 + 1/3 of leftover..
that implies 2/3rds is left for Chloe..
if 2/3 of leftover = $32
1/3 of leftover = $16
$16+$4 = $20.
Your way was still much simpler!
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logitech wrote:A) 4 + (x-4)/2
B) 4 + 1/3 [(X-12)/2]
C) 2/3 [(X-12)/2] = 32 ; (x-12) = 3 x 32
SO 4 + 1/3 [(X-12)/2] = 4+ 1/3 ( 3x32/2) = 20
If X is the total amount.
Ann : 4 + (x-4)/2 (Ann receives $4 plus one-half of what remains)
Bob : 4 + 1/3(x- Share of Ann) (Bob receives $4 plus one-third of what remains)
Bob: 4+1/3[x-(4+(x-4)/2)]
Isn't it?
How did you get 4 + 1/3 [(X-12)/2] ?
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I started with $100.
Ann receives a $4 plus one half of what remains -> 4 + 96/2 = 52.
Remaining = 100-52 = 48.
Bob receives $4 plus one third of what remains -> 4 + 44/3 = 56/3
Chloe receives the remaining $32. In this case Chloe receives 48 - 4 - 44/3 = 44*2/3.
Therefore, 44*2/3 equivalent to 32
and 56/3 (Bob's share) equivalent to (32*(56/3)*3)/(44*2) ~= 20.
Hence A.
Ann receives a $4 plus one half of what remains -> 4 + 96/2 = 52.
Remaining = 100-52 = 48.
Bob receives $4 plus one third of what remains -> 4 + 44/3 = 56/3
Chloe receives the remaining $32. In this case Chloe receives 48 - 4 - 44/3 = 44*2/3.
Therefore, 44*2/3 equivalent to 32
and 56/3 (Bob's share) equivalent to (32*(56/3)*3)/(44*2) ~= 20.
Hence A.