# Lesson 1

Proportional Relationships and Equations

Let’s write equations describing proportional relationships.

### Problem 1

A certain ceiling is made up of tiles. Every square meter of ceiling requires 10.75 tiles. Fill in the table with the missing values.

square meters of ceiling | number of tiles |
---|---|

1 | |

10 | |

100 | |

\(a\) |

### Problem 2

On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled in miles, \(d\), to the number of hours flying, \(t\), is \(t = \frac{1}{500} d\). How long will it take the airplane to travel 800 miles?

### Problem 3

Each table represents a proportional relationship. For each, find the constant of proportionality, and write an equation that represents the relationship.

\(s\) | \(P\) |
---|---|

2 | 8 |

3 | 12 |

5 | 20 |

10 | 40 |

Constant of proportionality:

Equation: \(P =\)

\(d\) | \(C\) |
---|---|

2 | 6.28 |

3 | 9.42 |

5 | 15.7 |

10 | 31.4 |

Constant of proportionality:

Equation: \(C =\)

### Problem 4

Diego bought 12 mini muffins for $4.20.

- At this rate, how much would Diego pay for 4 mini muffins?
- How many mini muffins could Diego buy with $3.00? Explain or show your reasoning. If you get stuck, consider using the table.

number of mini muffins |
price in dollars |
---|---|

12 | 4.20 |

### Problem 5

It takes \(1\frac{1}{4}\) minutes to fill a 3-gallon bucket of water with a hose. At this rate, how long does it take to fill a 50-gallon tub? If you get stuck, consider using a table.