Question

Business is booming for Lena's house cleaning service, Clean Your Scene, and she needs to hire more house cleaners.
This table shows the relationship between the number of new house cleaners Lena hires, x, and the total number of houses her company can clean per week, y.
x (new house cleaners) y (total houses)
2 28
6 44
17 88
19 96
According to the values in the table, do x and y have a proportional relationship?
yes
no

Answer 1

To determine whether \( x \) (the number of new house cleaners) and \( y \) (the total houses cleaned) have a proportional relationship, we can check if the ratio \( \frac{y}{x} \) remains constant for the given values.

Let's calculate the ratios for each pair of values in the table:

1. For \( x = 2 \) and \( y = 28 \):
\[
\frac{y}{x} = \frac{28}{2} = 14
\]

2. For \( x = 6 \) and \( y = 44 \):
\[
\frac{y}{x} = \frac{44}{6} \approx 7.33
\]

3. For \( x = 17 \) and \( y = 88 \):
\[
\frac{y}{x} = \frac{88}{17} \approx 5.18
\]

4. For \( x = 19 \) and \( y = 96 \):
\[
\frac{y}{x} = \frac{96}{19} \approx 5.05
\]

Since the ratios are not constant (14, approximately 7.33, approximately 5.18, and approximately 5.05), we conclude that \( x \) and \( y \) do not have a proportional relationship.

The answer is **no**.