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

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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

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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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New post 12 Mar 2015, 11:59
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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

Answer 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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New post 12 Mar 2015, 14:31
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
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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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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

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

Answer: C

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

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New post 12 Mar 2015, 21:04
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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
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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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New post 15 Mar 2015, 21:38
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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.


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)
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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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New post 24 Jul 2015, 11:38
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

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Sam's car was fined for parking when he gave Joe and Peter a ride [#permalink]

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New post 06 Jun 2017, 17:49
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
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Re: Sam's car was fined for parking when he gave Joe and Peter a ride [#permalink]

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New post 06 Jun 2017, 23:32
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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Re: Sam’s car was fined when he gave Joe and Peter a ride, so they decided [#permalink]

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New post 07 Jun 2017, 06:56
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


Merging topics. Please refer to the discussion above.
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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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New post 07 Jun 2017, 07:16
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.

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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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New post 10 Jun 2017, 07:33
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.

Answer: 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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New post 10 Jun 2017, 15:52
[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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New post 23 Sep 2017, 03:45
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.

Answer = (C)


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, 03:45
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