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.

Answer 1

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)