Math CentralQuandaries & Queries


Question from Awotil:

A fraction whose denominator is more than the numerator is double when the numerator is increased by 6 and the denominator is increased by 5 find the original fraction?


Are you sure you have sent the entire question? The way it is worded it has many solutions, in fact infinitely many.

Suppose the fraction is $\large \frac{a}{b}.$ If you increase the numerator by 6 and the denominator by 5 then you get $\large \frac{a+6}{b+5}.$ This new fraction is double the original and hence

\[\frac{a+6}{b+5} = 2 \times \frac{a+6}{b+5}.\]

Solve this equation to find $a$ in terms of $b.$

Now for whatever value of $b$ you choose this equation give a corresponding value of $a$ so that $\large \frac{a}{b}$ satisfies the condition you want.


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