Question

If a number is added to the numerator of 5/6 and twice as much is added to the denominator, the result is 3/5. Find the number.

Answer 1

We are given that a number is added to the numerator of 5/6. If "x" is the number then this can be written mathematically as:

$\frac{5+x}{6}$

we also told that twice this number is added to the denominator, this can be written mathematically as:

$\frac{5+x}{6+2x}$

We are also told that the result of this operation of 3/5, therefore, we have:

$\frac{5+x}{6+2x}=\frac{3}{5}$

We get an equation with one variable. To solve this equation we will cross multiply the equation, like this:

$5(5+x)=3(6+2x)$

Now we will apply the distributive property on both parentheses:

$25+5x=18+6x$

Now we subtract 6x from both sides:

$\begin{gathered} 25+5x-6x=18+6x-6x \\ 25-x=9 \end{gathered}$

Now we subtract 25 from both sides:

$\begin{gathered} 25-25-x=18-25 \\ -x=-7 \end{gathered}$

Now we multiply both sides by -1:

$x=7$

Therefore, the number is 16.

Let's replace the value of "x" in the expression: