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.