# Lesson 4

Proportional Relationships and Equations

### 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
$$a$$

### Solution

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### 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?

### Solution

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### 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: $$C =$$

### Solution

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### Problem 4

A map of Colorado says that the scale is 1 inch to 20 miles or 1 to 1,267,200. Are these two ways of reporting the scale the same? Explain your reasoning.

### Solution

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(From Unit 1, Lesson 11.)

### Problem 5

Here is a polygon on a grid.

1. Draw a scaled copy of the polygon using a scale factor 3. Label the copy A.

2. Draw a scaled copy of the polygon with a scale factor $$\frac{1}{2}$$. Label it B.

3. Is Polygon A a scaled copy of Polygon B? If so, what is the scale factor that takes B to A?

### Solution

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(From Unit 1, Lesson 3.)