Adding a Percent

A price with 25% tax added: the price is x, the tax is 25% of it, 0.25x, and together they come to 10. As an equation:

x + 0.25x = 10

x and 0.25x are like terms (x is 1x), so they collect: 1.25x = 10. Divide by 1.25: x = 8. Check: 8 plus a quarter of 8 is 10.

"A number plus 25% of itself" is always 1.25x; "a number minus 20% of itself" is 0.8x. Collecting the like terms first turns every percent-increase problem into a one-step equation.