Question

A closet organizer charges a $100 initial consultation fee plus $30 per hour. The cost as a function of the number of hours worked is 0 hours costs $100, 2 hours worked is $150, 3 hours worked is $200, 5 hours worked is $250, and 6 hours worked is $300. Write an equation that represents the cost as a function of the number of hours.

Answer 1

Let's say the number of hours worked is represented by x.
For the first 0 hours, the cost is $100. This can be written as:
Cost = 100
For 2 hours worked, the cost is $150. We can write it as:
Cost = 100 + (2 * 30) = 100 + 60 = 160
Similarly, for 3 hours worked, the cost is $200. We can write it as:
Cost = 100 + (3 * 30) = 100 + 90 = 190
For 5 hours worked, the cost is $250. We can write it as:
Cost = 100 + (5 * 30) = 100 + 150 = 250
Finally, for 6 hours worked, the cost is $300. We can write it as:
Cost = 100 + (6 * 30) = 100 + 180 = 280
From the given information, we can see that the cost increases by $30 for every hour worked. Therefore, the equation representing the cost as a function of the number of hours is:
Cost = 100 + (30 * x)