Adding a Percent

Suppose a price has 25% tax added, and the total is 10. The price is $x$. The tax is 25% of the price, which is $0.25x$. The price and the tax together come to 10, so the equation is:

$$x+0.25x = 10$$

$x$ and $0.25x$ are like terms, because $x$ is $x$. Add them: $1.25x = 10$. Divide both sides by 1.25: $x = 8$. Check the answer: 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 $0.8x$. When you add the like terms first, a percent-increase problem becomes a one-step equation.