# The numerator of a fraction is twice the denominator.What is the fraction if the numerator is doubled and the denominator is decreased by three and the value of the ratio is 5/3?

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Let the denominator be x:

Then the numerator = 2x

Then the fraction is 2x/x

Now, if the numerator doubled ==> 2(2x)

and the cenomenator is decreased by 3==> x-3

The the new fraction is : 4x/(x-3)

Given the ratio = 5/3

==> 4x/(x-3) = 5/3

Now let us cross multiply:

==> 3*4x = 5(x-3)

==> 12x = 5x - 15

==> 7x = -15

==> x= -15/7

==> 2x= -30/7

Then the fractions is: 2x/x = -30/7 / -15/7 = 2/1

Let:

Denominator of the original fraction = x

Then:

Original fraction = 2x/x

Doubling the numerator and decreasing the denominator by 3:

Revised fraction = (2*2x)/(x - 3) = 5/3 (given)

==> 4x/(x - 3) = 5/3

==> 3*4x = 5(x - 3)

==> 12x = 5x - 15

==>12x - 5x = -15

==> 7x = -15

Therefore:

x = -15/7

We get the value of original fraction by substituting value of x in 2x/x:

Original fraction = (2*(-15/7)]/-15/7 = (- 30/7)/(-15/7)

Pleas note that though simplifying the fraction will result in value 2/1. this simplified fraction will not meet the conditions described in the question.

According to enunciation, we'll put the denominator as x and the numerator as 2x.

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

2(2x) (1)

If we'll decrease the denominator by 3, we'll have:

x - 3 (2)

We'll divide (1) by (2) and we'll get 5/3:

2(2x)/(x - 3) = 5/3

We'll cross multiply and we'll get:

12x = 5(x-3)

We'll remove the brackets:

12x = 5x - 15

We'll subtract 5x both sides:

7x = -15

We'll divide by 7 both sides:

x = -15/7

The original ratio is 2x/x = 2, so it doesn't matter whatis the value of x, the quotient is a constant.