Sean, Tim, Fred and Mark paid a total of $132 for a souvenir. Mark paid 3/8 of what the rest paid. Sean paid 20% of what the rest paid. Tim and Fred paid an equal amount of money. How much did Fred pay?

Answer 1

Fred's amount --- x
Tim's amount ---- x
Mark's amount --- y
Sean's amount --- z

Mark paid 3/8 of what the rest paid ---> y = (3/8)(132 - 2x - z)
8y = 396 - 6x - 3z
6x + 8y + 3z = 396 , #1

Sean paid 20% of what the rest paid ---> z = (1/5)(132-2x-y)
5z = 132 - 2x - y
2x + y + 5z = 132 , #2

2x + y + z = 132 , #3

I get x = 66 , y = 0, z = 0

Perhaps I misinterpreted the "what the rest paid" part of the question

Fred-- 66
Tim --- 66
which adds up to 132, and the rest paid 0
3/8 of 0 is 0
1/5 of 0 is 0
so 66 + 66 + 0 + 0 = 132 , my answer meets the conditions

Answer 2

x = 1/5 (2y + 2)
5x - 2y - 2 = 0 —> (1)
z = 3/8 (2y + x)
8z = 8y + 3x —> (2)
x + 2y + z = 132 —> (3)
we get 3
40x - 11y - 82 = 0
3x + 6y - 82 = 0
— — 4
————————-
37x - 22y = 0
x = 22/37y
y = 37
8x + 16y + 8z = 10
3x + 16y - 8 = 0
+ + -
————————
11x + 22y = 1056
x = 22 z = 36
Fred paid $37