## How to Translate and Solve Applications

Contents

In most of the application problems we solved earlier, we were able to find the quantity we were looking for by simplifying an algebraic expression. Now we will be using equations to solve application problems. We’ll start by restating the problem in just one sentence, assign a variable, and then translate the sentence into an equation to solve. When assigning a variable, choose a letter that reminds you of what you are looking for.

## Example

The Robles family has two dogs, Buster and Chandler. Together, they weigh \(71\) pounds.

Chandler weighs \(28\) pounds. How much does Buster weigh?

### Solution

Read the problem carefully. | |

Identify what you are asked to find, and choose a variable to represent it. | How much does Buster weigh? Let \(b=\) Buster’s weight |

Write a sentence that gives the information to find it. | Buster’s weight plus Chandler’s weight equals 71 pounds. |

We will restate the problem, and then include the given information. | Buster’s weight plus 28 equals 71. |

Translate the sentence into an equation, using the variable \(b\). | |

Solve the equation using good algebraic techniques. | |

Check the answer in the problem and make sure it makes sense. | |

Is 43 pounds a reasonable weight for a dog? Yes. Does Buster’s weight plus Chandler’s weight equal 71 pounds? | |

\(43+28\stackrel{?}{=}71\) | |

\(71=71\phantom{\rule{0.2em}{0ex}}✓\) | |

Write a complete sentence that answers the question, “How much does Buster weigh?” | Buster weighs 43 pounds |

### How to Devise a problem-solving strategy.

- Read the problem. Make sure you understand all the words and ideas.
- Identify what you are looking for.
- Name what you are looking for. Choose a variable to represent that quantity.
- Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.
- Solve the equation using good algebra techniques.
- Check the answer in the problem and make sure it makes sense.
- Answer the question with a complete sentence.

## Example

Shayla paid \(\text{\$24,575}\) for her new car. This was \(\text{\$875}\) less than the sticker price. What was the sticker price of the car?

### Solution

What are you asked to find? | “What was the sticker price of the car?” |

Assign a variable. | Let \(s=\) the sticker price of the car. |

Write a sentence that gives the information to find it. | $24,575 is $875 less than the sticker price $24,575 is $875 less than \(s\) |

Translate into an equation. | |

Solve. | |

Check: | |

Is $875 less than $25,450 equal to $24,575? | |

\(25,450-875\stackrel{?}{=}24,575\) | |

\(24,575=24,575\phantom{\rule{0.2em}{0ex}}✓\) | |

Write a sentence that answers the question. | The sticker price was $25,450. |