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

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.

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

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

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

 

­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.