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# Sam’s car was fined when he gave Joe and Peter a ride, so they decided

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Math Expert
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Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink]

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12 Mar 2015, 05:46
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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.
[Reveal] Spoiler: OA

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Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink]

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12 Mar 2015, 10:59
1
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Joe=1/4f+3
Peter= 1/3f-3

Sam=1/2f-4

We can find F=48

Thus Sam paid 24-4=20

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Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink]

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12 Mar 2015, 13:31
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
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Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink]

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12 Mar 2015, 15:17
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Bunuel wrote:
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.

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

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he gave Joe and Peter a ride, so they decided [#permalink]

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12 Mar 2015, 20:04
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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 _________________ Kindly press "+1 Kudos" to appreciate Math Expert Joined: 02 Sep 2009 Posts: 43804 Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink] ### Show Tags 15 Mar 2015, 20:38 1 This post received KUDOS Expert's post Bunuel wrote: 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. 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 = [(1/4)F + 3] + [(1/3)F – 3] + [(1/2)F – 4] 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) _________________ Intern Joined: 30 Sep 2013 Posts: 22 Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink] ### Show Tags 24 Jul 2015, 10:38 Bunuel wrote: 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. 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 [1][/2]*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 Director Joined: 04 Dec 2015 Posts: 696 Location: India Concentration: Technology, Strategy Schools: ISB '19, IIMA , IIMB, XLRI WE: Information Technology (Consulting) Re: Sam's car was fined for parking when he gave Joe and Peter a ride [#permalink] ### Show Tags 06 Jun 2017, 22:32 mkrishnabdrr wrote: Sam's car was fined for parking 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 Sam$4 less than 1/2 the fine to complete the payment. How much did Sam pay?
A. 48
B. 24
C. 20
D. 15
E. 50

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...

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Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink]

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07 Jun 2017, 06:16
sashiim20 wrote:
mkrishnabdrr wrote:
Sam's car was fined for parking 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 Sam $4 less than 1/2 the fine to complete the payment. How much did Sam pay? A. 48 B. 24 C. 20 D. 15 E. 50 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... 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 _________________ If you like my posts, please give kudos. Help me unlock gmatclub tests. Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 1975 Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink] ### Show Tags 10 Jun 2017, 06:33 Bunuel wrote: 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 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.

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Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink]

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10 Jun 2017, 14:52
[quote="Bunuel"]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/quote]

let f=amount of fine
13/12*f-4=f
f=$48 Sam's share=f/2-4=$20
C
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Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink]

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23 Sep 2017, 02:45
Bunuel wrote:
Bunuel wrote:
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.

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 = [(1/4)F + 3] + [(1/3)F – 3] + [(1/2)F – 4]
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.

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.
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Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided   [#permalink] 23 Sep 2017, 02:45
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