Question

Could the relationship between the cost and the number of hours be proportional?
Number of Hours (h) Cost (c) Cost per Hour (
h
c
​
)
9 $18.00 $2.00
17 $63.75 $3.75
27 $121.50 $4.50

The relationship could be proportional.

The relationship could not be proportional.

Answer 1

To determine whether the relationship between the cost (c) and the number of hours (h) is proportional, we need to check if the ratio of cost to hours is constant.

Let's look at the cost per hour calculated for each case:

1. For 9 hours:
\[
\text{Cost per hour} = \frac{18.00}{9} = 2.00
\]

2. For 17 hours:
\[
\text{Cost per hour} = \frac{63.75}{17} \approx 3.75
\]

3. For 27 hours:
\[
\text{Cost per hour} = \frac{121.50}{27} \approx 4.50
\]

Now let's summarize the results:
- For 9 hours, cost per hour is $2.00.
- For 17 hours, cost per hour is $3.75.
- For 27 hours, cost per hour is $4.50.

The cost per hour is not constant—it changes as the number of hours increases.

Since the ratio of cost to hours is not constant, the relationship between the cost and the number of hours **could not be proportional**.