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

Question

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

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

KarishmaB · Accepted Answer

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

khaynes3 · Answer

(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

subhashghosh · Answer

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.

PareshGmat · Answer

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

JeffTargetTestPrep · Answer

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

Neghineh · Answer

I don't understand any of the answers... Anyone care to explain it more detailed to me?

a191291r · Answer

Yes. Let's break down the question.

A certain fraction is equivalent to 2/5.

Let the numerator be  x  and denominator be  y

We have  \frac{x}{y}=\frac{2}{5}

We can rewrite this as x in terms of y, we have  x=\frac{2y}{5}  --------(1)

If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3.

Increasing numerator by 4 makes it  x+4  and doubling denominator makes it  2*y  and after doing this, the fraction becomes 1/3

\frac{x+4}{2*y}=\frac{1}{3}

in order to simplify this, we multiply both sides by 6y, which gives

3x+12 = 2y

substituting value of x from equation (1), we get
 3*(\frac{2y}{5})+12=2y

solving the above gives  y=15

substituting in equation (1)

we have  x = \frac{2*15}{5} = 6

we have original fraction  \frac{x}{y }= \frac{6}{15}

What is the sum of the numerator and denominator of the original fraction?  
 Numerator + Denominator = x+y = 6+15 = 21

Answer is E

Hope this is clear.

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

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