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## Word problems

tagged by: rolandprowess

This topic has 1 expert reply and 0 member replies

### Top Member

BTGmoderatorRO Moderator
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#### Word problems

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

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
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Sun Oct 01, 2017 3:11 am
Roland2rule 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?
A. 40
B. 90
C. 130
D. 140
E. 150
Since A, B and C each contribute to the total cost, we get:
T = A + B + C.

If Archie had paid twice as much as he did pay, Betty and Coach would have each paid ten dollars less.
Thus:
T = 2A + (B-10) + (C-10)
T = 2A + B + C - 20.

Since the blue expressions above both represent the total cost, they must be equal:
2A + B + C - 20 = A + B + C
A = 20.

Coach paid twice as much as Archie.
Thus, C = 2A = 2*20 = 40.

Archie paid seventy dollars less than the difference between what Betty and Coach paid.
Thus:
A = (B-C) - 70.
Substituting A=20 and C=40 into A = (B-C) - 70, we get:
20 = B - 40 - 70
130 = B.

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