# Lesson 6

Using Equations to Solve Problems

Let’s use equations to solve problems involving proportional relationships.

### Problem 1

A car is traveling down a highway at a constant speed, described by the equation \(d = 65t\), where \(d\) represents the distance, in miles, that the car travels at this speed in \(t\) hours.

- What does the 65 tell us in this situation?
- How many miles does the car travel in 1.5 hours?
- How long does it take the car to travel 26 miles at this speed?

### Problem 2

Elena has some bottles of water that each holds 17 fluid ounces.

- Write an equation that relates the number of bottles of water (\(b\)) to the total volume of water (\(w\)) in fluid ounces.
- How much water is in 51 bottles?
- How many bottles does it take to hold 51 fluid ounces of water?

### Problem 3

There are about 1.61 kilometers in 1 mile. Let \(x\) represent a distance measured in kilometers and \(y\) represent the same distance measured in miles. Write two equations that relate a distance measured in kilometers and the same distance measured in miles.

### Problem 4

In Canadian coins, 16 quarters is equal in value to 2 toonies.

number of quarters | number of toonies |
---|---|

1 | |

16 | 2 |

20 | |

24 |

- Complete the table.
- What does the value next to 1 mean in this situation?

### Problem 5

Each table represents a proportional relationship. For each table:

- Fill in the missing parts of the table.
- Draw a circle around the constant of proportionality.

\(x\) | \(y\) |
---|---|

2 | 10 |

15 | |

7 | |

1 |

\(a\) | \(b\) |
---|---|

12 | 3 |

20 | |

10 | |

1 |

\(m\) | \(n\) |
---|---|

5 | 3 |

10 | |

18 | |

1 |

### Problem 6

Describe some things you could notice in two polygons that would help you decide that they were not scaled copies.