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A certain fraction is equivalent to 2/5. If the numerator of

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A certain fraction is equivalent to 2/5. If the numerator of  [#permalink]

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New post 15 Mar 2011, 15:54
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A certain fraction is equivalent to 2/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3. What is the sum of the numerator and denominator of the original fraction?

(A) 49
(B) 35
(C) 28
(D) 26
(E) 21
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Re: A certain fraction is equivalent to 2/5. If the numerator of  [#permalink]

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New post 15 Mar 2011, 19:28
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Even though there is nothing wrong with what you have done, try and use as few variables as possible. It reduces confusion and the number of steps required.
Since the fraction is equal to 2/5, lets say it is 2x/5x (x is the common integer that gets canceled to give 2/5)
\(\frac{(2x+4)}{2*5x} = \frac{1}{3}\)
x = 3
The original fraction is 2*3/5*3 = 6/15
Sum of numerator and denominator is 6+15 = 21
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Re: A certain fraction is equivalent to 2/5. If the numerator of  [#permalink]

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New post 15 Mar 2011, 19:03
(1) x/y = 2/5
(2) (x+4)/2y = 1/3

(1) 5x = 2y
(2) (x+4)/(2*((5/2)*x)) = 1/3
(2) (x+4)/5x = 1/3
(2) 3x+12 = 5x
(2) 12 = 2x
from (2) x = 6
substitute into y to get y = (5/2)*6 = 15

we're looking for x + y = 6 + 15 = 21

(E) 21
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Re: A certain fraction is equivalent to 2/5. If the numerator of  [#permalink]

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New post 15 Mar 2011, 21:30
x/y = 2/5 -> 1

(x+4)/2y = 1/3 -> 2

Divide 1 by 2 :

=> 2x/(x+4) = 6/5

=> 5x = 3x + 12

=> x = 6

=> y = 5/2 * 6 = 15

so x + y = 21

The answer is E.
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Re: A certain fraction is equivalent to 2/5. If the numerator of  [#permalink]

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New post 26 Jun 2014, 01:22
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Say the fraction \(= \frac{2x}{5x}\)

We require to find 5x + 2x = 7x

\(\frac{2x+4}{10x} = \frac{1}{3}\)

x = 3

7x = 21

Answer = E
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Re: A certain fraction is equivalent to 2/5. If the numerator of  [#permalink]

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New post 20 Jul 2017, 16:31
banksy wrote:
A certain fraction is equivalent to 2/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3. What is the sum of the numerator and denominator of the original fraction?

(A) 49
(B) 35
(C) 28
(D) 26
(E) 21


We can create the following equations in which the numerator = 2x and the denominator = 5x.

(2x + 4)/10x = 1/3

3(2x + 4) = 10x

6x + 12 = 10x

12 = 4x

x = 3

Since x = 3, the original numerator = 2(3) = 6 and the original denominator = 5(3) = 15. Thus, their sum is 6 + 15 = 21.

Answer: E
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Re: A certain fraction is equivalent to 2/5. If the numerator of  [#permalink]

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Re: A certain fraction is equivalent to 2/5. If the numerator of   [#permalink] 26 Feb 2019, 22:50
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