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Amy, Betty, and Chris paid a total of $135 for a common party. If Amy

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Amy, Betty, and Chris paid a total of $135 for a common party. If Amy  [#permalink]

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New post 25 Sep 2018, 04:10
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Amy, Betty, and Chris paid a total of $135 for a common party. If Amy paid (3/5)th of what Chris paid, Betty paid $51 and Chris paid the rest, what fraction of the total amount did Chris pay?


(A) 3/7
(B) 1/5
(C) 2/15
(D) 7/18
(E) 11/18

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Re: Amy, Betty, and Chris paid a total of $135 for a common party. If Amy  [#permalink]

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New post 25 Sep 2018, 06:18
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Bunuel wrote:
Amy, Betty, and Chris paid a total of $135 for a common party. If Amy paid (3/5)th of what Chris paid, Betty paid $51 and Chris paid the rest, what fraction of the total amount did Chris pay?


(A) 3/7
(B) 1/5
(C) 2/15
(D) 7/18
(E) 11/18


Let C = the amount Chris paid
So, (3/5)C = 0.6C = the amount Amy paid
And $51 = the amount Betty paid

In total, the 3 people spent $135
So, we can write: C + 0.6C + 51 = 135
Subtract 51 from both sides to get: C + 0.6C = 84
Simplify to get: 1.6C = 84
So, C = 84/1.6 = 52.5
So, Chris paid $52.5 of the total amount of $135

What fraction of the total amount did Chris pay?
Fraction is as follows: 52.5/135
Multiply top and bottom by 2 to get: 105/270
Divide top and bottom by 5 to get: 21/54
Divide top and bottom by 3 to get: 7/18

Answer: D

Cheers,
Brent
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Re: Amy, Betty, and Chris paid a total of $135 for a common party. If Amy  [#permalink]

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New post 25 Sep 2018, 12:44
Bunuel wrote:
Amy, Betty, and Chris paid a total of $135 for a common party. If Amy paid (3/5)th of what Chris paid, Betty paid $51 and Chris paid the rest, what fraction of the total amount did Chris pay?


(A) 3/7
(B) 1/5
(C) 2/15
(D) 7/18
(E) 11/18



let the amount of chris be x

we can form equation:

(3/5)x + x + 51 = 135

8x / 5 = 54

x = 52.5

Question : the amount chris paid / total amount = 52.5 / 135 = 105 / 270 = 7/18.

The best answer is D.
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Re: Amy, Betty, and Chris paid a total of $135 for a common party. If Amy  [#permalink]

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New post 25 Sep 2018, 14:13
Bunuel wrote:
Amy, Betty, and Chris paid a total of $135 for a common party. If Amy paid (3/5)th of what Chris paid, Betty paid $51 and Chris paid the rest, what fraction of the total amount did Chris pay?


(A) 3/7
(B) 1/5
(C) 2/15
(D) 7/18
(E) 11/18

\(\left. \begin{gathered}
C = \$ \,5k \hfill \\
A = \$ \,3k\,\, \hfill \\
B = \$ 51 \hfill \\
\end{gathered} \right\}\,\,\,\,\,\,8k + 51 = 135\,\,\,\,\,\,\,\,\,\left( {k > 0} \right)\)

\(? = \frac{{5k}}{{135}}\,\mathop = \limits^{\left( * \right)} \,\,\frac{k}{{27}}\)

\(\left( * \right)\,\,\,\frac{{135}}{5} = \underleftrightarrow {\frac{{100}}{5} + \frac{{35}}{5}} = 27\,\,\,\,\, \Rightarrow \,\,\,\,\,135 = 5 \cdot 27\)


\(8k = \underleftrightarrow {135 - \left( {35 + 16} \right)} = 84\,\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits_{{\text{FOCUS}}\,\,!}^{:\,\,\left( {8\, \cdot \,27} \right)} \,\,\,\,\,\,\,\,? = \frac{{8k}}{{8 \cdot 27}} = \underleftrightarrow {\frac{{84}}{{8 \cdot 27}}} = \frac{{4 \cdot 3 \cdot 7}}{{8 \cdot 3 \cdot 9}} = \frac{7}{{18}}\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: Amy, Betty, and Chris paid a total of $135 for a common party. If Amy  [#permalink]

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New post 27 Sep 2018, 16:35
Bunuel wrote:
Amy, Betty, and Chris paid a total of $135 for a common party. If Amy paid (3/5)th of what Chris paid, Betty paid $51 and Chris paid the rest, what fraction of the total amount did Chris pay?


(A) 3/7
(B) 1/5
(C) 2/15
(D) 7/18
(E) 11/18



We can let Chris’s amount = n, Amy’s amount = 3n/5, and Betty’s amount = 51; thus:

n + 3n/5 + 51 = 135

n + 3n/5 = 84

Multiplying the equation by 5, we obtain:

5n + 3n = 420

8n = 420

n = 52.5

So Chris paid 52.5/135 = 525/1350 = 105/270 = 21/54 = 7/18.

Answer: D
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Re: Amy, Betty, and Chris paid a total of $135 for a common party. If Amy &nbs [#permalink] 27 Sep 2018, 16:35
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Amy, Betty, and Chris paid a total of $135 for a common party. If Amy

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