# 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. 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
dollars
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.)