# The numerator of a fraction is three less than the denominator.What is the fraction if the numerator is tripled and denominator is increased by 7 , the value of resulting fraction is 3/2 ?

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We assume x is the numerator.

Then the denomiator = x+3.

The fraction is x/(x+3)

The fraction obtained by tripling numearator and the increasing the denominator by 7 is 3x/(x+3+7) = 3x/(x+10) but this fraction is equal to 3/2.

Therefore 3x/(x+10) = 3/2

Multiply by (x+10)*2 both sides:

3x*2 = 3*(x+10)

6x = 3x+30

6x-3x = 30

3x = 30

x = 30/3 = 10

Therefore the original fraction = x/(x+3) = 10/13.

Tally : 3x/(x+10) = 10*3/(13+7) = 30/20 = 3/2.

Let the fraction be X/Y.

Now we are given that the numerator is 3 less than the denominator or X = Y - 3.

Also, we know that is the numerator is tripled and the denominator is increased by 7 the function we have is 3/2

=> X*3 / (Y + 7)

=> 3/2

=> (Y - 3)*3/ (Y + 7) = 3/2

=> (3Y - 9)/ (Y+7) = 3/2

=> 2*(3Y - 9) = 3*(Y+7)

=> 6Y - 18 = 3Y + 21

=> 3Y = 39

=> Y = 13

=> X = 10

**Therefore the fraction we started with was 10/13**

According to enunciation, we'll put the denominator as x and the numerator as x-3.

If we'll triple the numerator, we'll get:

3(x-3) (1)

If we'll increase the denominator by 7, we'll have:

x + 7 (2)

We'll divide (1) by (2) and we'll get 3/2:

3(x-3)/(x + 7) = 3/2

We'll divide by 3 both sides:

(x-3)/(x + 7) = 1/2

We'll cross multiply and we'll get:

x+7 = 2(x-3)

We'll remove the brackets:

x + 7 = 2x - 6

We'll subtract 2x both sides:

-x +7 = -6

We'll subtract 7 both sides:

-x = -13

We'll multiply by -1:

x = 13

Since the original ratio was (x-3)/x, we'll substitute x and we'll calculate the value of the original ratio:

(x-3)/x = (13-3)/13

**(x-3)/x = 10/13**