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The denominator of a fraction is 3 more than its numerator.

When 1/2 is added to this fraction, the resulting fraction's denominator is twice the denominator of the original fractions and its numerator is 1 more than its denominator.

What is the numerator of the original fraction?

1 Answer

3 votes

Answer:

Numerator of the original fraction is 1

Explanation:

Let's assume numerator of fraction as 'y'

denominator of fraction as 'x'

so, fraction is


(y)/(x)

The denominator of a fraction is 3 more than its numerator

so,
x=y+3

When 1/2 is added to this fraction, the resulting fraction's denominator is twice the denominator of the original fractions and its numerator is 1 more than its denominator

so,


(y)/(x)+(1)/(2)=(x+1)/(2x)

we can use first equation and plug x


(y)/(y+3)+(1)/(2)=(y+3+1)/(2(y+3))

now, we can solve for y

we get


(y)/(y+3)\cdot \:2\left(y+3\right)+(1)/(2)\cdot \:2\left(y+3\right)=(y+4)/(2\left(y+3\right))\cdot \:2\left(y+3\right)


3y+3=y+4


2y=1


y=(1)/(2)

now, we can find x


x=(1)/(2)+3


x=(7)/(2)

now, we can find fraction


(y)/(x)=((1)/(2) )/((7)/(2))


(y)/(x) =(1)/(7)

So,

Numerator is 1

User Jonathanpberger
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