Business is booming for Lena's house cleaning service, Clean Your Scene, and she needs to hire more house cleaners.

Question

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 if \( x \) (the number of new house cleaners hired) and \( y \) (the total number of houses cleaned per week) have a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) remains constant for the given values.

Calculating the ratios based on the table:

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

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

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

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

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

Answer: no