Percent Equations

Take the sentence "20% of a number is 15". Percent means per hundred, so 20% is $\frac{20}{100}$, which is $\frac{1}{5}$ or 0.2. The word "of" means multiply. So the sentence becomes the equation:

$$20\%x = 15$$

Write the percent as a fraction over 100, and the equation has a fraction coefficient: $\frac{1}{5}x = 15$. Multiply both sides by 5 to get $x = 75$. Check the answer: a fifth of 75 is 15.

Every "what number" percent question has this shape. "12 is 30% of what?" becomes $30\%x = 12$. "What is 15% of 80?" becomes $x = 15\%\cdot 80$, and that needs no solving, only arithmetic. Write the sentence as an equation, then solve it the way you already know.