## Solving Applications Using Proportions

The strategy for solving applications that we have used earlier in this tutorial, also works for proportions, since proportions are equations. When we set up the **proportion**, we must make sure the units are correct—the units in the numerators match and the units in the denominators match.

## Example

When pediatricians prescribe acetaminophen to children, they prescribe \(5\) milliliters (ml) of acetaminophen for every \(25\) pounds of the child’s weight. If Zoe weighs \(80\) pounds, how many milliliters of acetaminophen will her doctor prescribe?

### Solution

Identify what you are asked to find. | How many ml of acetaminophen the doctor will prescribe |

Choose a variable to represent it. | Let \(a=\) ml of acetaminophen. |

Write a sentence that gives the information to find it. | If 5 ml is prescribed for every 25 pounds, how much will be prescribed for 80 pounds? |

Translate into a proportion. | |

Substitute given values—be careful of the units. | |

Multiply both sides by 80. | |

Multiply and show common factors. | |

Simplify. | |

Check if the answer is reasonable. | |

Yes. Since 80 is about 3 times 25, the medicine should be about 3 times 5. | |

Write a complete sentence. | The pediatrician would prescribe 16 ml of acetaminophen to Zoe. |

You could also solve this proportion by setting the cross products equal.

## Example

One brand of microwave popcorn has \(120\) calories per serving. A whole bag of this popcorn has \(3.5\) servings. How many calories are in a whole bag of this microwave popcorn?

### Solution

Identify what you are asked to find. | How many calories are in a whole bag of microwave popcorn? |

Choose a variable to represent it. | Let \(c=\) number of calories. |

Write a sentence that gives the information to find it. | If there are 120 calories per serving, how many calories are in a whole bag with 3.5 servings? |

Translate into a proportion. | |

Substitute given values. | |

Multiply both sides by 3.5. | |

Multiply. | |

Check if the answer is reasonable. | |

Yes. Since 3.5 is between 3 and 4, the total calories should be between 360 (3⋅120) and 480 (4⋅120). | |

Write a complete sentence. | The whole bag of microwave popcorn has 420 calories. |

## Example

Josiah went to Mexico for spring break and changed \(\text{\$325}\) dollars into Mexican pesos. At that time, the exchange rate had \(\text{\$1}\) U.S. is equal to \(12.54\) Mexican pesos. How many Mexican pesos did he get for his trip?

### Solution

Identify what you are asked to find. | How many Mexican pesos did Josiah get? |

Choose a variable to represent it. | Let \(p=\) number of pesos. |

Write a sentence that gives the information to find it. | If \$1 U.S. is equal to 12.54 Mexican pesos, then \$325 is how many pesos? |

Translate into a proportion. | |

Substitute given values. | |

The variable is in the denominator, so find the cross products and set them equal. | |

Simplify. | |

Check if the answer is reasonable. | |

Yes, \$100 would be \$1,254 pesos. \$325 is a little more than 3 times this amount. | |

Write a complete sentence. | Josiah has 4075.5 pesos for his spring break trip. |