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

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.

  1. At this rate, how much would Diego pay for 4 mini muffins?
  2. 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
12 4.20
(From Unit 2, Lesson 9.)

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.

(From Unit 2, Lesson 10.)