SEARCH HOME
 Math Central Quandaries & 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?

Hi,

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.

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.