Sara works in an ice cream shop. The table shows the number of hours she worked during each of the past four weeks and the amount she earned each week.

Question

Time Worked Amount Earned
(hours) (dollars)
15 127.50
16.5 140.25
12.5 106.25
17 144.50

Let t represent the time in hours and let a represent the amount earned in dollars. Which equation models the relationship between these variables?

Answer 1

The equation that models the relationship between time worked and amount earned is:

a = 7.5t + 100

This is a linear equation of the form y = mx + b, where t is the independent variable (time worked), a is the dependent variable (amount earned), m is the slope (rate of pay per hour, which is $7.50), and b is the y-intercept (base pay, which is $100).

The equation shows that for every hour worked, Sara earns $7.50 on top of her base pay of $100. For example, if she works 20 hours, her earnings would be:

a = 7.5(20) + 100
a = 150 + 100
a = 250

Therefore, Sara would earn $250 for working 20 hours.