Question

After an increase of 7 in both numerator as well as the denominator, the fraction changes to 3/4. What was the original fraction?

Answer 1

Step-by-step explanation:

let numerator be x and denominator be y

x+7/y+7=3/4

3(x+7)=4(y+7)

3x+21=4y+28

x+y=7

Answer 2

After an increase of 7 in both numerator as well as the denominator, the fraction changes to 3/4. The original fraction is 2/5

Solution:

Let the original fraction be,

$Original\ fraction = \frac{x}{y}$

After an increase of 7 in both numerator as well as the denominator, the fraction changes to 3/4

Therefore,

$\frac{x+7}{y+7} = \frac{3}{4}\\\\Cross\ multiply\\\\4(x+7) = 3(y+7)\\\\Expand\\\\4x + 28 = 3y + 21\\\\4x-3y = 21-28\\\\4x-3y = -7\\\\4x + 7 = 3y$

There are many possible fractions that can satisfy the above equation.

Let us find the minimum value of x for which the the value of y is an integer

Substitute x = 1

4(1) + 7 = 3y

4 + 7 = 3y

3y = 11

y = 11/3

11/3 could not be an integer

Now substitute x = 2

4(2) + 7 = 3y

15 = 3y

y = 5

Therefore, the original fraction is:

$Original\ fraction = \frac{2}{5}$

Thus similarly, there are many possible fractions

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