## Subtracting Integers in Applications

Contents

It’s hard to find something if we don’t know what we’re looking for or what to call it. So when we solve an application problem, we first need to determine what we are asked to find. Then we can write a phrase that gives the information to find it. We’ll translate the phrase into an expression and then simplify the expression to get the answer. Finally, we summarize the answer in a sentence to make sure it makes sense.

### Solving Application Problems:

- Identify what you are asked to find.
- Write a phrase that gives the information to find it.
- Translate the phrase to an expression.
- Simplify the expression.
- Answer the question with a complete sentence.

## Example

The temperature in Urbana, Illinois one morning was \(11\) degrees Fahrenheit. By mid-afternoon, the temperature had dropped to \(-9\) degrees Fahrenheit. What was the difference between the morning and afternoon temperatures?

### Solution

Step 1. Identify what we are asked to find. | the difference between the morning and afternoon temperatures |

Step 2. Write a phrase that gives the information to find it. | the difference of \(11\) and \(-9\) |

Step 3. Translate the phrase to an expression. The word | \(11-\left(-9\right)\) |

Step 4. Simplify the expression. | \(20\) |

Step 5. Write a complete sentence that answers the question. | The difference in temperature was \(20\) degrees Fahrenheit. |

Geography provides another application of negative numbers with the elevations of places below sea level.

## Example

Dinesh hiked from Mt. Whitney, the highest point in California, to Death Valley, the lowest point. The elevation of Mt. Whitney is \(14,497\) feet above sea level and the elevation of Death Valley is \(282\) feet below sea level. What is the difference in elevation between Mt. Whitney and Death Valley?

### Solution

Step 1. What are we asked to find? | The difference in elevation between Mt. Whitney and Death Valley |

Step 2. Write a phrase. | elevation of Mt. Whitney−elevation of Death Valley |

Step 3. Translate. | \(14,497-\left(-282\right)\) |

Step 4. Simplify. | \(14,779\) |

Step 5. Write a complete sentence that answers the question. | The difference in elevation is \(14,779\) feet. |

Managing your money can involve both positive and negative numbers. You might have **overdraft** protection on your checking account. This means the bank lets you write checks for more money than you have in your account (as long as they know they can get it back from you!)

## Example

Leslie has \(\text{$25}\) in her checking account and she writes a check for \(\text{$8.}\)

- What is the balance after she writes the check?
- She writes a second check for \(\text{$20.}\) What is the new balance after this check?
- Leslie’s friend told her that she had lost a check for \(\text{$10}\) that Leslie had given her with her birthday card. What is the balance in Leslie’s checking account now?

### Solution

What are we asked to find? | The balance of the account |

Write a phrase. | \($25\) minus \($8\) |

Translate | |

Simplify. | |

Write a sentence answer. | The balance is \($17\). |

What are we asked to find? | The new balance |

Write a phrase. | \($17\) minus \($20\) |

Translate | |

Simplify. | |

Write a sentence answer. | She is overdrawn by \($3\). |

What are we asked to find? | The new balance |

Write a phrase. | \($10\) more than \(-$3\) |

Translate | |

Simplify. | |

Write a sentence answer. | The balance is now \($7\). |

### Optional Video: Integer Application: Overdrawn Checking Account