Question

a home cleaning service takes more time to clean larger spaces. the table shows the number of minutes it takes for the service to clean a certain number of square feet within a home.
square feet and cleaning time
number of square feet, x: 50, 80, 100, 150
time in minutes, y: 20, 32, 40, 60
based on the table, how many minutes would it take for the service to clean 200 square feet?
20 minutes
80 minutes
125 minutes
400 minutes

Explanation:

Step1: Check Proportionality

Calculate the ratio of \( y \) to \( x \) for each pair:

• \( \frac{20}{50} = 0.4 \)
• \( \frac{32}{80} = 0.4 \)
• \( \frac{40}{100} = 0.4 \)
• \( \frac{60}{150} = 0.4 \)

The ratio is constant (\( y = 0.4x \)), so it’s a proportional relationship.

Step2: Calculate Time for 200 sq ft

Use \( y = 0.4x \). Substitute \( x = 200 \):
\( y = 0.4 \times 200 = 80 \).

Answer:

80 minutes