Math Help - Percents

1. Percents

A number is increased by 25% and the resulting number is then decreased by 20%. The final number is what percent of the original number?

I know the answer is 100 but how do I show it?

2. Originally Posted by donnagirl
A number is increased by 25% and the resulting number is then decreased by 20%. The final number is what percent of the original number?

I know the answer is 100 but how do I show it?
Dear donnagirl,

Suppose your number is x, then when it is increased by 25% the resulting number is,

$x+\frac{25x}{100}$

Then the result is decreased by 20% that is,

$\left(x+\frac{25x}{100}\right)-\frac{20}{100}\left(x+\frac{25x}{100}\right)=\frac {5x}{4}-\frac{1}{5}\left(\frac{5x}{4}\right)=x$

So the number is 100% of the original number.