BTGModeratorVI wrote: ↑Sun Jul 19, 2020 1:36 pm
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
Answer:
B
Source: Magoosh
Notice that we need not consider Ann's portion in the solution. We can just let K = 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
Bob received 4 dollars plus one-third of what remained
Once Bob receives $4, the amount remaining is K-4 dollars. So, Bob gets a 1/3 of that as well.
1/3 of K-4 is (K-4)/3
So ALTOGETHER, Bob receives
4 + (K-4)/3
So, our equation becomes:
K - [4 + (K-4)/3 ] = 32
Simplify to get: K - 4 - (K-4)/3 = 32
Multiply both sides by 3 to get: 3K - 12 - K + 4 = 96
Simplify: 2K - 8 = 96
Solve: K = 52
Plug this K-value into
K - Bob's $ = 32 to get: 52 - Bob's $ = 32
So, Bob's $ = 20
Answer: B
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