Four friends split their lunch bill such that Ken paid $9 more than

Question

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

A. $84
B. $120
C. $144
D. $180
E. $216

BrentGMATPrepNow · Accepted Answer

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

GMATinsight · Answer

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

pushpitkc · Answer

Let the total amount paid be x

Now coming to the individual split's we use the information given in the question stem

Ken's split = x/6 + 9 = 10x/60 + 9
Justin's split = 2x/5 - 8 = 24x/60 - 8
Dan's split = x/12 + 1 = 5x/60 + 1
Melissa's split = 40$

Total = Ken's split + Justin's split + Dan's split + Mellisa's split
x = 39x/60 +42
21x/60 = 42
x = 120(Option B)

sashiim20 · Answer

Let Total bill be  T .
Ken paid  = 9 + \frac{1}{6}T 
Justin paid  = \frac{2}{5}T - 8 
Dan paid  = 1 + \frac{1}{12}T 
Melissa paid  = $40

T = 40 + 9 + \frac{1}{6}T + \frac{2}{5}T - 8 + 1 + \frac{1}{12}T = 42 + \frac{10T + 24T + 5T}{60} = \frac{39T}{60} + 42

T - \frac{39T}{60} = 42  ==>  60T - 39T = 42*60  ==>  21T = 42*60

T = \frac{42*60}{21}

T = $120  .  Answer B...

chetan2u · Answer

Hi,

of course the method above by all is the one to find answer, at times a bit of logic can get the answer for you or get you close to the answer, if you are clueless..
 
the fractions given are 1/6 , 2/5, 1/12...
so our answer has to be MULTIPLE of LCM of 6,5,12, or multiple of 60
ONLY B and D are left..
atleast the probability has come up to 50% from 20%, in some other Q it may just give you the answer

tlaw · Answer

K = T/6 + 9
J = 2T/5 - 8
D = T/12 + 1
M = 40

K+J+D+M = T
Solve for T.

T = K+J+D+M 
T = T/6 + 9 + 2T/5 - 8 + T/12 + 1 + 40 
T= 39T/60 + 42 
21T/60T = 42
T = 120

Abhishek009 · Answer

LCM of 6, 5 & 12 = 60

So, the total bill amount must be a multiple of 60 ,  Only options (B) and (D) remains..

Check any one option to mark the answer...

Let's check option (B) -

Total Bill amount is 120
Ken paid = 29
Justin paid = 40
Dan paid = 11
Melissa paid = 40

Total = 29+40+11+40 = 120 
  
Hence, (B) is the correct answer...

ScottTargetTestPrep · Answer

We can let the total bill = t.
 
Ken paid 9 + (1/6)t, Justin paid (2/5)t - 8, Dan paid (1/12)t + 1, and Melissa paid 40. Thus:
 
9 + (1/6)t + (2/5)t - 8 + (1/12)t + 1 + 40 = t
 
42 + (1/6)t + (2/5)t + (1/12)t = t
 
Multiplying the equation by 60, we have:
 
2,520 + 10t + 24t + 5t = 60t
 
2520 = 21t
 
120 = t
 
Answer: B

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