Problem Solving

BTGmoderatorRO wrote: ↑

Sat Sep 30, 2017 7:28 pm

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?
A. 40
B. 90
C. 130
D. 140
E. 150
qa is c.
i know the answer is between D and E but i don't know the simple approach i can use. Can you help me out with the solution

The key to solving this problem is this sentence: “If Archie had paid twice as much as he did pay, Betty and Coach would have each paid ten dollars less.” This means that Betty and Coach together would have paid 20 dollars less, which means that Archie would have paid 20 dollars more than he paid. Since the extra 20 dollars would have resulted in Archie’s paying twice as much, he must have paid 20 dollars originally (so that the doubled amount would be 40 dollars).

Since Archie paid 20 dollars and Coach paid twice as much, Coach paid 40 dollars.

Since Betty paid the most and Archie paid seventy dollars less than the difference between what Betty and Coach paid, if we let x = the amount Betty paid, we have:

20 = x - 40 - 70

130 = x

Answer: C