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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?

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, 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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12 Mar 2015, 16:17

1

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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?

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?

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.

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

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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

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

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08 Feb 2017, 19:54

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

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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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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; \(x = \frac{1}{4}x + 3 + \frac{1}{3}x - 3 + \frac{1}{2}x - 4\)

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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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; \(x = \frac{1}{4}x + 3 + \frac{1}{3}x - 3 + \frac{1}{2}x - 4\)

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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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

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, 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?

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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