Seth, Andy and Ben shared a sum of money. The amount received by Andy was 5/6 the amount of money received by Ben. After Seth had given $42 to Andy and $22 to Ben, Andy gave $4 to Ben. In the end, 3 of them had the same amount of money. Find the difference between the amount of money that Seth and Andy had at first.
Let's call the amount of money received by Ben "x". Then we know that Andy received 5/6 of x, or (5/6)x. And Seth must have received the remaining amount, which is x - (5/6)x, or (1/6)x.
So, the total amount they shared is:
x + (5/6)x + (1/6)x = (4/3)x
After Seth gave $42 to Andy and $22 to Ben, the amounts they had become:
Andy: (5/6)x + 42
Ben: x + 22
When Andy gave $4 to Ben, their amounts became:
Andy: (5/6)x + 42 - 4 = (5/6)x + 38
Ben: x + 22 + 4 = x + 26
We know that in the end, they all had the same amount of money. Let's call this amount "y". Then we can set up two equations:
(4/3)x - 42 - 22 = y
(5/6)x + 38 - 4 = y
Simplifying these equations, we get:
(4/3)x - 64 = y
(5/6)x + 34 = y
Setting the two equations equal to each other and solving for x, we get:
(4/3)x - 64 = (5/6)x + 34
Multiplying both sides by 6, we get:
8x - 384 = 5x + 204
Solving for x, we get:
x = 196
So Ben received $196, Andy received $5/6 x $196 = $163.33 (rounded to the nearest cent), and Seth received the remaining amount, which is $36.67 (rounded to the nearest cent).
After Seth gave $42 to Andy and $22 to Ben, their amounts became:
Andy: $163.33 + $42 - $4 = $201.33
Ben: $196 + $22 = $218
In the end, they all had the same amount of money, so each had:
$201.33 + $218 + $36.67 = $456
The difference between the amount of money that Seth and Andy had at first is:
$201.33 - $36.67 = $164.66 (rounded to the nearest cent)