Rental

Explanation

We will carefully read the problem and use the given facts to write them in the form of a percent sentence.  Then we can translate the sentence into a percent equation and solve it to find the unknown number of units in the complex.

We can write

198 is 88% of what number?

198 = 88% • x

Now we solve the equation.

• Write 88% as a decimal: 88% = 0.88
  • 198 = 0.88 • x
• To undo the multiplication by 0.88 and isolate x on the right side, divide both sides of the equation by 0.88.
  • \(\frac{198}{\color{red}{0.88}} = \frac{0.88 \cdot x}{\color{red}{0.88}}\)
• To simplify the fraction on the right side of the equation, remove the common factor of 0.88 from the numerator and denominator.  On the left side, divide 198 by 0.88
  • \(\require{cancel} \frac{198}{0.88} = \frac{\cancel{0.88}^1 \cdot x}{\cancel{0.88_1}}\)
• 225 = x

The apartment complex has 225 units, of which 198, or 88%, are occupied.