## How to Translate and Solve Percent Proportions

Contents

Now that we have written percent equations as proportions, we are ready to solve the equations.

## Example

Translate and solve using proportions: What number is \(\text{45%}\) of \(80?\)

### Solution

Identify the parts of the percent proportion. | |

Restate as a proportion. | |

Set up the proportion. Let \(n=\) number. | |

Find the cross products and set them equal. | |

Simplify. | |

Divide both sides by 100. | |

Simplify. | |

Check if the answer is reasonable. | |

Yes. 45 is a little less than half of 100 and 36 is a little less than half 80. | |

Write a complete sentence that answers the question. | 36 is 45% of 80. |

In the next example, the percent is more than \(100,\) which is more than one whole. So the unknown number will be more than the base.

## Example

Translate and solve using proportions: \(\text{125%}\) of \(25\) is what number?

### Solution

Identify the parts of the percent proportion. | |

Restate as a proportion. | |

Set up the proportion. Let \(n=\) number. | |

Find the cross products and set them equal. | |

Simplify. | |

Divide both sides by 100. | |

Simplify. | |

Check if the answer is reasonable. | |

Yes. 125 is more than 100 and 31.25 is more than 25. | |

Write a complete sentence that answers the question. | 125% of 25 is 31.25. |

Percents with decimals and money are also used in proportions.

## Example

Translate and solve: \(\text{6.5%}\) of what number is \(\text{\$1.56}?\)

### Solution

Identify the parts of the percent proportion. | |

Restate as a proportion. | |

Set up the proportion. Let\(n=\) number. | |

Find the cross products and set them equal. | |

Simplify. | |

Divide both sides by 6.5 to isolate the variable. | |

Simplify. | |

Check if the answer is reasonable. | |

Yes. 6.5% is a small amount and \$1.56 is much less than \$24. | |

Write a complete sentence that answers the question. | 6.5% of \$24 is \$1.56. |

## Example

Translate and solve using proportions: What percent of \(72\) is \(9?\)

### Solution

Identify the parts of the percent proportion. | |

Restate as a proportion. | |

Set up the proportion. Let \(n=\) number. | |

Find the cross products and set them equal. | |

Simplify. | |

Divide both sides by 72. | |

Simplify. | |

Check if the answer is reasonable. | |

Yes. 9 is \(\frac{1}{8}\) of 72 and \(\frac{1}{8}\) is 12.5%. | |

Write a complete sentence that answers the question. | 12.5% of 72 is 9. |