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Buy "All-In-One Standard ($149)", get free Daily quiz (2 mon). Coupon code : SPECIAL # Ann, Carol, and Judy paid a total of$45 for their dinner at a restaur

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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 $$= \frac{20}{45} = \frac{4}{9}$$

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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

$$\frac{20}{45} = \frac{4}{9}$$

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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.

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Re: Ann, Carol, and Judy paid a total of $45 for their dinner at a restaur [#permalink] ### Show Tags 04 Sep 2018, 06:47 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: Ann, Carol, and Judy paid a total of$45 for their dinner at a restaur   [#permalink] 04 Sep 2018, 06:47
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