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Four friends split their lunch bill such that Ken paid $9 more than 1/
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07 Apr 2021, 05:21
07 Apr 2021, 05:21
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Question Stats:
80% (02:17) correct
20% (02:44) wrong based on 15 sessions
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Four friends split their lunch bill such that Ken paid $9 more than 1/6 of the total, Justin paid $8 less than 2/5 of the total, Dan paid $1 more than 1/12 of the total, and Melissa paid the remaining $40. How much was the total bill?
A. $84
B. $120
C. $144
D. $180
E. $216
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. $84
B. $120
C. $144
D. $180
E. $216
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Joined: 10 Apr 2015
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Re: Four friends split their lunch bill such that Ken paid $9 more than 1/
[#permalink]
07 Apr 2021, 05:49
07 Apr 2021, 05:49
1
Carcass wrote:
Four friends split their lunch bill such that Ken paid $9 more than 1/6 of the total, Justin paid $8 less than 2/5 of the total, Dan paid $1 more than 1/12 of the total, and Melissa paid the remaining $40. How much was the total bill?
A. $84
B. $120
C. $144
D. $180
E. $216
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. $84
B. $120
C. $144
D. $180
E. $216
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Let B = total cost of the bill
Ken paid $9 more than 1/6 of the total
So, (1/6)B + 9 = amount Ken paid
Justin paid $8 less than 2/5 of the total
So, (2/5)B - 8 = amount Justin paid
Dan paid $1 more than 1/12 of the total
So, (1/12)B + 1 = amount Dan paid
Melissa paid the remaining $40
40 = amount Melissa paid
We know that TOTAL amount = (Ken's amount) + (Justin's amount) + (Dan's amount) + (Melissa's amount)
So we get: B = (1/6)B + 9 + (2/5)B - 8 + (1/12)B + 1 + 40
Simplify: B = (1/6)B + (2/5)B + (1/12)B + 42
Multiply both sides by 60 (the LCM of 6, 5 and 12) to get: 60B = 10B + 24B + 5B + 2520
Simplify: 60B = 39B + 2520
So, 21B = 2520
B = 120
Answer: B
Cheers,
Brent
Re: Four friends split their lunch bill such that Ken paid $9 more than 1/
[#permalink]
08 Apr 2021, 06:29
08 Apr 2021, 06:29
x = Lunch Bill
Ken = 9 + (x/6)
Justin = (2x/5) - 8
Dan = 1 + (x/12)
Melissa = 40
Total Bill = x = 9 + (x/6)+ (2x/5) - 8 + 1 + (x/12) + 40
i.e. x = 13x/20 + 42
i.e. (7/20)x = 42
x = 120
Answer: option B
Ken = 9 + (x/6)
Justin = (2x/5) - 8
Dan = 1 + (x/12)
Melissa = 40
Total Bill = x = 9 + (x/6)+ (2x/5) - 8 + 1 + (x/12) + 40
i.e. x = 13x/20 + 42
i.e. (7/20)x = 42
x = 120
Answer: option B
