Sams car was fined when he gave Joe and Peter a ride, so they decided

Question

Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $3 more than 1/4 of the fine and Peter paid $3 less than 1/3 of the fine, leaving pay $4 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?

A. $13
B. $15
C. $20
D. $28
E. $48

Kudos for a correct solution.

A. $13 
B. $15 
C. $20 
D. $28 
E. $48

Kudos for a correct  solution .

vasili · Answer

Joe=1/4f+3
Peter= 1/3f-3

Sam=1/2f-4

We can find F=48

Thus Sam paid 24-4=20

Answer C

23a2012 · Answer

the answer is C
let say the total fine=T
so Joe paid 3+T/4
Peter paid T/3-3
sam paied T/2-4
T=(3+T/4)+(T/3-3)+(T/2-4)
T=48
sam paied=20

peachfuzz · Answer

(1/4)x + 3 + (1/3)x - 3 + (1/2)x -4 = x
x=48
1/2(48) - 4 = 20

Answer: C

PareshGmat · Answer

Answer = C. $20

Sam .......... Joe ................. Peter .................. Total

\frac{x}{2} - 4  .........  \frac{x}{4} + 3  ...........  \frac{x}{3} - 3  ............ x (Say total fine = x)

Setting up the equation with above variables

\frac{x}{2} + \frac{x}{4} + \frac{x}{3} - x = 4

x = 48

Sam's contribution = 24-4 = 20

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

Call the fine F. Joe paid (1/4)F + 3 and Peter paid (1/3)F – 3, leaving (1/2)F – 4 left. If we add those three up, they should add up to F.
F =   +   +  
F = (1/4)F + (1/3)F + (1/2)F – 4

Multiply all terms by 12 to clear the fractions.
12F = 3F + 4F + 6F – 48
12F = 13 F – 48
–F = – 48
F = 48

Well, if the fine cost $48, then Sam paid the part not covered by Joe or Peter. Half the fine is $24, and Sam paid $4 less than this: $20.

Answer = (C)

riteshgmat · Answer

I did the same way as most of the people have done. I have also solved in the following way, a little bit reverse thing, please let me know if I am doing wrong here.

As given sam' payment is   *Fine -4
i.e Total Fine = 2 * (Sam's payment + 4)

Now, as everything looks integer, Fine should be able to divide by 4 and 3 . Because Joe's contribution has 1/4 of the fine and Peter's contribution has 1/3 of the fine

So, that leads me to following :

Options , Sam's pay , Total Fine (F) , F/4 , F/3

A) , 13 , 34 , No i.e 34/4 , No i.e 34/3

B) , 14 , 38 , No , No

C) , 20 , 48 , Yes Yes
,
No need to further go on as we have got F/4 and F/3 correct, just for confirmation we go further

D) , 28 , 64 , Yes , No

E) , 48 , 104 , Yes , No

So we can see the Option C has the correct values

sashiim20 · Answer

Let the fine be x Joe paid = \frac{1}{4}x + 3 Peter paid = \frac{1}{3}x - 3 Sam has to pay = \frac{1}{2}x - 4 From the question; x = \frac{1}{4}x + 3 + \frac{1}{3}x - 3 + \frac{1}{2}x - 4 x = \frac{1}{4}x + \frac{1}{3}x + \frac{1}{2}x - 4 x = \frac{3x + 4x + 6x}{12} - 4 = \frac{13x}{12} - 4 \frac{13x}{12} - x = 4 \frac{13x - 12x}{12} = \frac{x}{12} = 4 x = 12 * 4 = 48 . Answer A... _________________ Kindly press "+1 Kudos" to appreciate

Mkrishnabdrr · Answer

Question stem asks for how much did sam pay: So, Sam has to pay = \frac{1}{2}x - 4 =1/2 x 48 -4 =24-4 =20 Hence, Ans is C. You found out the fine. _________________ Kindly press "+1 Kudos" to appreciate

JeffTargetTestPrep · Answer

We can let t = the total amount of the fine.
 
Joe’s payment = 3 + (1/4)t
 
Peter’s payment = (1/3)t - 3
 
Sam’s payment = (1/2)t - 4
 
We can create the following equation to determine t:
 
3 + (1/4)t + (1/3)t - 3 + (1/2)t - 4 = t
 
(1/4)t + (1/3)t + (1/2)t - 4 = t
 
Multiplying by 12, we have:
 
3t + 4t + 6t - 48 = 12t
 
48 = t
 
Thus, Sam paid (1/2)(48) - 4 = 24 - 4 = $20.
 
Answer: C

gracie · Answer

Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $3 more than 1/4 of the fine and Peter paid $3 less than 1/3 of the fine, leaving pay $4 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?

A. $13
B. $15
C. $20
D. $28
E. $48

Kudos for a correct solution.

A. $13 
B. $15 
C. $20 
D. $28 
E. $48/quote]

let f=amount of fine
13/12*f-4=f
f=$48
Sam's share=f/2-4=$20
C

ashikaverma13 · Answer

Hi,

I don't understand. Doesn't the question say what 'fraction' of the fine did sam say? Here, we're stating his share of the fine.

BrentGMATPrepNow · Answer

Let F = the total cost of the fine

Joe paid $3 more than 1/4 of the fine  
So, F/4 + 3 = the amount Joe paid

Peter paid $3 less than 1/3 of the fine  
So, F/3 - 3 = the amount Peter paid

Sam paid $4 less than 1/2 the fine  
So, F/2 - 4 = the amount Sam paid

(amount Joe paid) + (amount Peter paid) + (amount Sam paid) = total cost of fine
We can write: (F/4 + 3) + (F/3 - 3 ) + (F/2 - 4) = F
To eliminate the fractions, we'll multiply both sides of the equation by 12 (the least common multiple of 3, 4 and 2)
When we do this, we get: 3F + 36 + 4F - 36 + 6F - 48 = 12F
Simplify to get: 13F - 48 = 12F
Solve:  F = 48

What fraction of the fine did Sam pay?  
F/2 - 4 = the amount Sam paid
So,  48 /2 - 4 = the amount Sam paid
Evaluate to see that  Sam paid $20

Answer: C

ASIDE: the question asks   What  fraction  of the fine did Sam pay?  
So, the answer SHOULD be 20/ 48

Cheers,
Brent

Rogermoris · Answer

let say the total fine=F, where 
1) Joe paid  3+ \frac{T}{4} 
2) Peter paid  \frac{T}{3} -3 
3) Sam paid  \frac{T}{2} -4

The individual fines paid by them is added to obtain the actual fine. 
 T=(3+\frac{T}{4})+(\frac{T}{3}-3)+(\frac{T}{2}-4) 
T=48

Thus Sam paid  \frac{T}{2}-4 = 20

stne · Answer

right  Brent  , if the question is asking for a fraction then answer should be  \frac{20}{48} .
Hope Moderator makes the necessary correction.

Sams car was fined when he gave Joe and Peter a ride, so they decided

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