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Ann, Carol, and Judy paid a total of $45 for their dinner at a restaur

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Ann, Carol, and Judy paid a total of $45 for their dinner at a restaur  [#permalink]

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New post 30 Jun 2017, 02:26
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E

Difficulty:

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Question Stats:

87% (01:51) correct 13% (02:31) wrong based on 89 sessions

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Ann, Carol, and Judy paid a total of $45 for their dinner at a restaurant. If Ann paid (2/5)th of what Judy paid, Carol paid $17 and Judy paid the rest, what fraction of the total amount did Judy pay?

(A) 2/9
(B) 14/45
(C) 1/3
(D) 2/5
(E) 4/9

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Re: Ann, Carol, and Judy paid a total of $45 for their dinner at a restaur  [#permalink]

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New post 30 Jun 2017, 02:48
Bunuel wrote:
Ann, Carol, and Judy paid a total of $45 for their dinner at a restaurant. If Ann paid (2/5)th of what Judy paid, Carol paid $17 and Judy paid the rest, what fraction of the total amount did Judy pay?

(A) 2/9
(B) 14/45
(C) 1/3
(D) 2/5
(E) 4/9


Let Judy paid be \(= x\)

Ann paid \(= \frac{2}{5}x\)

Carol paid \(= $17\)

Total Bill \(= $45\)

Total bill = Ann paid + Judy paid + Carol paid

\(45 = x + \frac{2}{5}x + 17\)

\(x + \frac{2}{5}x = 45 - 17 => 28\)

\(\frac{5x + 2x}{5} = 28\)

\(7x = 28*5\)

\(x = \frac{140}{7} = 20\)

Therefore Judy paid \(= $20\)

Required fraction = Amount Judy paid / Total Bill \(= \frac{20}{45} = \frac{4}{9}\)

Answer (E)...
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Re: Ann, Carol, and Judy paid a total of $45 for their dinner at a restaur  [#permalink]

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New post 30 Jun 2017, 03:12
1
Bunuel wrote:
Ann, Carol, and Judy paid a total of $45 for their dinner at a restaurant. If Ann paid (2/5)th of what Judy paid, Carol paid $17 and Judy paid the rest, what fraction of the total amount did Judy pay?

(A) 2/9
(B) 14/45
(C) 1/3
(D) 2/5
(E) 4/9


Let's Assume Judy's share is = 5x
So, Ann's share would be = \(\frac{2}{5}\) 5x = 2x

Thus,
2x + 5x + 17 = 45
2x + 5x = 28
7x = 28
x = 4

Judy's Contribution = 5x = 5.4 = 20
Judy's Contribution (%) = \(\frac{20}{45}\) = \(\frac{4}{9}\)

Hence Answer E
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Ann, Carol, and Judy paid a total of $45 for their dinner at a restaur  [#permalink]

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New post 30 Jun 2017, 06:02
Bunuel wrote:
Ann, Carol, and Judy paid a total of $45 for their dinner at a restaurant. If Ann paid (2/5)th of what Judy paid, Carol paid $17 and Judy paid the rest, what fraction of the total amount did Judy pay?

(A) 2/9
(B) 14/45
(C) 1/3
(D) 2/5
(E) 4/9

Lots of ways to solve this one, but we have a total dollar amount, a dollar amount for Carol, and one of the two remaining variables is defined in terms of the other. Substitution here is quick and easy.

A = \(\frac{2}{5}\)J

A + J + C = 45

A + J = 45 - 17, substitute A = \(\frac{2}{5}\)J

\(\frac{2}{5}\)J + J = 28, multiply all by 5

2J + 5J = 140

7J = 140

J = 20, J's fraction of the total amount is

\(\frac{20}{45} = \frac{4}{9}\)

Answer E
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Re: Ann, Carol, and Judy paid a total of $45 for their dinner at a restaur  [#permalink]

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New post 30 Jun 2017, 08:13
Bunuel wrote:
Ann, Carol, and Judy paid a total of $45 for their dinner at a restaurant. If Ann paid (2/5)th of what Judy paid, Carol paid $17 and Judy paid the rest, what fraction of the total amount did Judy pay?

(A) 2/9
(B) 14/45
(C) 1/3
(D) 2/5
(E) 4/9


Let contributions be -

Judy = \(5x\)
Ann = \(2x\)
Carol = \($ 17\)

SO, we have \(5x + 2x + 17 = 45\)

Or, \(7x = 28\)

Or, \(x = 4\)

So, Judy paid 20 ...

Quote:
what fraction of the total amount did Judy pay?


= \(\frac{20}{45}\)

= \(\frac{4}{9}\)

Thus, the correct answer must be (E) \(\frac{4}{9}\)
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Re: Ann, Carol, and Judy paid a total of $45 for their dinner at a restaur  [#permalink]

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New post 04 Jul 2017, 06:47
1
Bunuel wrote:
Ann, Carol, and Judy paid a total of $45 for their dinner at a restaurant. If Ann paid (2/5)th of what Judy paid, Carol paid $17 and Judy paid the rest, what fraction of the total amount did Judy pay?

(A) 2/9
(B) 14/45
(C) 1/3
(D) 2/5
(E) 4/9


We can let A = the amount Ann paid, C = the amount Carol paid, and J = the amount Judy paid and create the following equations:

A + C + J = 45

J = 45 - (A + C)

Since A = 2J/5 and C = 17, we have:

J = 45 - [2J/5 + 17]

J = 28 - 2J/5

5J = 140 - 2J

7J = 140

J = 20

Thus, Judy paid 20/45 = 4/9 of the total amount.

Answer: E
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Re: Ann, Carol, and Judy paid a total of $45 for their dinner at a restaur  [#permalink]

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Re: Ann, Carol, and Judy paid a total of $45 for their dinner at a restaur &nbs [#permalink] 04 Sep 2018, 06:47
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