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When the numerator of a fraction is increased by 4, the fraction increases by 2/3....

up vote 14 down vote favorite

When the numerator of a fraction is increased by $4$, the fraction increases by $2/3$. What is the denominator of the fraction?

I tried,

Let the numerator of the fraction be $x$ and the denominator be $y$.

Accordingly, $$\frac{x+4}y=\frac xy+\frac 23$$

I am not able to find the second equation.

2 Answers

up vote 4 down vote accept

Again, you've got a fine start:

You wrote: $$\frac{x+4}y=\color{red}{\frac xy}+\color{blue}{\frac 23}\tag{1}$$

But note that $$\frac{x+4}{y} = \color{red}{\frac xy} + \color{blue}{\frac 4y}\tag{2}$$

From $(1),(2),$ it must follow that $$\color{blue}{\frac 4y = \frac 23 } \iff 2y = 4\cdot 3 = 12 \iff y = \frac{12}{2} = 6$$

So the denominator, $y$ is $6$.

up vote 3 down vote

If you add 4 to the numerator, the value of your fraction will be increased by $\frac4y$, where y is your denominator.

So $\frac4y=\frac23$ and $y=6$


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When the numerator of a fraction is increased by 4, the fraction increases by 2/3....

up vote 14 down vote

When the numerator of a fraction is increased by $4$, the fraction increases by $2/3$. What is the denominator of the fraction?

I tried,

Let the numerator of the fraction be $x$ and the denominator be $y$.

Accordingly, $$\frac{x+4}y=\frac xy+\frac 23$$

I am not able to find the second equation.


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up vote 9 down vote

Again, you've got a fine start:

You wrote: $$\frac{x+4}y=\color{red}{\frac xy}+\color{blue}{\frac 23}\tag{1}$$

But note that $$\frac{x+4}{y} = \color{red}{\frac xy} + \color{blue}{\frac 4y}\tag{2}$$

From $(1),(2),$ it must follow that $$\color{blue}{\frac 4y = \frac 23 } \iff 2y = 4\cdot 3 = 12 \iff y = \frac{12}{2} = 6$$

So the denominator, $y$ is $6$.

edit

The value of $x$ is not determined by the given information. Now that you know $y = 6$, the statement of the problem says that $\frac{x+4}6=\frac x6 + \frac23$, which is true for all $x$. - David K 2 days ago

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