Three friends split their dinner bill such that Shay paid $7 less than half the total bill, Ashley paid $8 more than

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

Three friends split their dinner bill such that Shay paid $7 less than half the total bill, Ashley paid $8 more than

by BTGmoderatorDC » Tue Jul 28, 2020 7:13 pm

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Three friends split their dinner bill such that Shay paid $7 less than half the total bill, Ashley paid $8 more than 1/4 the total bill, and Jenna paid the remaining $20. How much was the total bill?

A. $72
B. $76
C. $80
D. $84
E. $88

OA D

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Tue Jul 28, 2020 7:13 pm

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Three friends split their dinner bill such that Shay paid $7 less than half the total bill, Ashley paid $8 more than

by Scott@TargetTestPrep » Fri Jul 31, 2020 6:42 am

BTGmoderatorDC wrote: ↑
Tue Jul 28, 2020 7:13 pm
Three friends split their dinner bill such that Shay paid $7 less than half the total bill, Ashley paid $8 more than 1/4 the total bill, and Jenna paid the remaining $20. How much was the total bill?

A. $72
B. $76
C. $80
D. $84
E. $88

OA D

Solution:

We can let b = the total bill.

Shay paid 7 dollars less than half the bill; thus:

Shay = (1/2)b - 7

Ashley paid 8 dollars more than (1/4) the total bill; thus:

Ashley = (1/4)b + 8

We also are given that the amount Jenna paid = 20. We can create the following equation to determine b:

Shay + Ashley + Jenna = total bill

(1/2)b - 7 + (1/4)b + 8 + 20 = b

(1/2)b + (1/4)b + 21 = b

(2/4)b + (1/4)b + 21 = b

(3b/4) + 21 = b

21 = b/4

b = 84

Answer: D

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