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If 1/(4x) + 1/y = 1/3*(1/x + 1/y), what is the ratio of x to y?

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If 1/(4x) + 1/y = 1/3*(1/x + 1/y), what is the ratio of x to y?  [#permalink]

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New post 18 Jul 2018, 00:50
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If \(\frac{1}{4x} + \frac{1}{y}=\frac{1}{3}*(\frac{1}{x} + \frac{1}{y})\), what is the ratio of x to y?

(A) 3 to 4
(B) 2 to 3
(C) 1 to 2
(D) 1 to 8
(E) 1 to 9

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Re: If 1/(4x) + 1/y = 1/3*(1/x + 1/y), what is the ratio of x to y?  [#permalink]

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New post 18 Jul 2018, 01:22
1
Bunuel wrote:
If \(\frac{1}{4x} + \frac{1}{y}=\frac{1}{3}*(\frac{1}{x} + \frac{1}{y})\), what is the ratio of x to y?


1/4x + 1/y = 1/3x + 1/3y

Solving we get,
1/4x - 1/3x = 1/3y - 1/y
y = 8x
x/y =1/8

Hence, D.
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Re: If 1/(4x) + 1/y = 1/3*(1/x + 1/y), what is the ratio of x to y?  [#permalink]

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New post 18 Jul 2018, 03:29
2

Solution



Given:
    • \(\frac{1}{4x}+ \frac{1}{y}= \frac{1}{3} * (\frac{1}{x} + \frac{1}{y})\)


To find:
• The ratio of x to y

Approach and Working:
• \(\frac{1}{4x}+ \frac{1}{y}= \frac{1}{3} * (\frac{1}{x} + \frac{1}{y})\)
• \(\frac{3}{4x}+\frac{3}{y}= \frac{1}{x}+\frac{1}{y}\)
• \(\frac{2}{y}=\frac{1}{x}-\frac{3}{4x}\)
• \(\frac{2}{y}= \frac{1}{4x}\)
• \(\frac{x}{y}= \frac{1}{8}\)




Hence, the correct answer is option D.

Answer: D
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Re: If 1/(4x) + 1/y = 1/3*(1/x + 1/y), what is the ratio of x to y?  [#permalink]

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New post 22 Jul 2018, 18:33
Bunuel wrote:
If \(\frac{1}{4x} + \frac{1}{y}=\frac{1}{3}*(\frac{1}{x} + \frac{1}{y})\), what is the ratio of x to y?

(A) 3 to 4
(B) 2 to 3
(C) 1 to 2
(D) 1 to 8
(E) 1 to 9


Simplifying, we have:

1/4x + 1/y = 1/3x + 1/3y

Multiplying by the common denominator 12xy, we have:

3y + 12x = 4y + 4x

8x = y

x/y = 1/8

Answer: D
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Re: If 1/(4x) + 1/y = 1/3*(1/x + 1/y), what is the ratio of x to y? &nbs [#permalink] 22 Jul 2018, 18:33
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