adam15 wrote:Archie, Betty and Coach bought a radio. Archie paid the least amount of money, Coach paid twice as much as Archie, and Betty paid the most. Archie paid seventy dollars less than the difference between what Betty and Coach paid. If Archie had paid twice as much as he did pay, Betty and Coach would have each paid ten dollars less. Which of the following equals the amount Betty paid?
40
90
130
140
Insufficient information
The question seems a bit ambiguous, but I'm going to interpret it as the three of them are splitting the cost of one radio.
With that in mind, we have:
A+B+C = R
C = 2A
A = (B - C) - 70
A = 20 (this is really the key to the question and comes from the "If Archie had paid twice as much as he did pay, Betty and Coach would have each paid ten dollars less." part of the problem - see below for full translation)
and 0 < A < B < C
We know that A=20
Therefore:
C = 2(20) = 40
and:
20 = (B - 40) - 70
20 = B - 110
130 = B... done!
* * *
Back to that key deduction that A=20.
We know that:
If Archie had paid twice as much as he did pay, Betty and Coach would have each paid ten dollars less.
Well, if Betty and Coach each pay 10 dollars less, that's a total of 20 extra dollars that A is paying. We can derive the following equation:
(New amount Archie paying) - (Old amount Archie was paying) = 20
Archie normally pays A dollars, so if he's paying twice as much, he's paying 2A dollars. Accordingly:
New amount = 2A
Old amount = A
and:
2A - A = 20
A = 20
