# Lesson 4

Comparing Relationships with Tables

### Problem 1

Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would the constant of proportionality be?

1. How loud a sound is depending on how far away you are.
distance to
listener (ft)
sound
level (dB)
5 85
10 79
20 73
40 67
2. The cost of fountain drinks at Hot Dog Hut.
volume
(fluid ounces)
cost
($) 16$1.49
20 $1.59 30$1.89

### Problem 2

A taxi service charges $1.00 for the first $$\frac{1}{10}$$ mile then$0.10 for each additional $$\frac{1}{10}$$ mile after that.

Fill in the table with the missing information then determine if this relationship between distance traveled and price of the trip is a proportional relationship.

distance traveled (mi) price (dollars)
$$\frac{9}{10}$$
2
$$3\frac{1}{10}$$
10

### Problem 3

A rabbit and turtle are in a race. Is the relationship between distance traveled and time proportional for either one? If so, write an equation that represents the relationship.

Turtle’s run:

distance (meters) time (minutes)
108 2
405 7.5
540 10
1,768.5 32.75

Rabbit’s run:

distance (meters) time (minutes)
800 1
900 5
1,107.5 20
1,524 32.5

### Problem 4

For each table, answer: What is the constant of proportionality?

a b
2 14
5 35
9 63
$$\frac13$$ $$\frac73$$
a b
3 360
5 600
8 960
12 1440
a b
75 3
200 8
1525 61
10 0.4
a b
4 10
6 15
22 55
3 $$7\frac12$$

### Solution

(From Unit 5, Lesson 1.)

### Problem 5

Here is a table that shows the ratio of flour to water in an art paste. Complete the table with values in equivalent ratios.

cups of flour cups of water
1 $$\frac12$$
4
3
$$\frac12$$