Daily GMAT Math Q - explain

[ejager]

Per today's daily GMAT Math Q:

A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives a $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

Expert reply-
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

I don't understand why in the equation K - B= 32, if B= 4+(k-4)/3
when you plug in B for K-B shouldn't the negative carry through to all terms?

So why isn't it:
K - (4+(k-4)/3 =32
K - 4 - K+4/3 = 32
K - K+4/3 = 36
K-K =O which doesn't make sense?

[Brent@GMATPrepNow]

A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives a $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

Expert reply-
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

I don't understand why in the equation K - B= 32, if B= 4+(k-4)/3
when you plug in B for K-B shouldn't the negative carry through to all terms?

So why isn't it:
K - (4+(k-4)/3 =32
K - 4 - K+4/3 = 32
K - K+4/3 = 36
K-K =O which doesn't make sense?

Hey, I wrote that question (https://www.beatthegmat.com/tough-word-p ... 27218.html)

The problem is above: K - 4 - K+4/3 = 32
It should be: K - 4 - (K-4)/3 = 32
The numerator k-4 is its own entity while part of the fraction.

Cheers,
Brent

[ejager]

The problem is above: K - 4 - K+4/3 = 32
It should be: K - 4 - (K-4)/3 = 32
The numerator k-4 is its own entity while part of the fraction.

In the second equation where does the second negative go if it doesn't affect (k-4)/3?
I don't understand why it shouldn't distribute out and then be
K - (K-4)/3 = 36
K - (K-4)= 108
K - K + 4 = 108
...? I know this is not the right answer but I don't get how to distribute the negative.

Thanks

[DavidG@VeritasPrep]

K - (K-4)/3 = 36
K - (K-4)= 108

This operation was where you went wrong. If you want to multiply both sides of the equation by 3, you'd go from

K - (K-4)/3 = 36

to

3* [K - (K-4)/3] = 36 * 3

or

3K - (K - 4) = 108

[Ian Stewart]

After we give Bob his $4, we know that he gets 1/3 of what's left, and Chloe gets 2/3 of what's left, so Chloe gets twice as much as Bob (not counting Bob's extra $4). Since Chloe got $32, Bob got $16. We need to add back Bob's additional $4, so the answer is $20.