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.
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)
To find the equation that represents the cost as a function of the number of hours worked, we need to examine the given information.
From the given information, we know that the initial consultation fee is $100. Additionally, for each hour worked, an additional $30 is charged.
Let's break down the information into steps:
1) For 0 hours worked, the cost is $100.
2) For 2 hours worked, the cost is $150.
3) For 3 hours worked, the cost is $200.
4) For 5 hours worked, the cost is $250.
5) For 6 hours worked, the cost is $300.
To express this pattern as an equation, we can say that the cost (C) is equal to the initial consultation fee ($100) plus the additional charge per hour (30) multiplied by the number of hours worked (H). Therefore, the equation is:
C = 100 + 30H
In this equation, C represents the cost of the closet organizer's services and H represents the number of hours worked.
To write an equation that represents the cost as a function of the number of hours, we need to consider the given information:
1. The initial consultation fee is $100.
2. The cost increases by $30 for each hour worked.
Based on these details, we can write the equation as follows:
Cost = $100 + ($30 × Number of Hours)
The initial $100 represents the consultation fee, and the $30 multiplied by the number of hours gives us the additional cost for the hours worked.