Tariq is a mechanic. He charges his customers by the hour. The first hour of service costs $122. The second hour of service costs $171.99. The third hour of service costs $221.98. Write an equation in the form of y=c +d (x -1) to represent this situation. Explain how you got your equation.
plz help
i need help to get the equation
171.99 - 122 = 49.99
221.98 - 171.99 = 49.99
Sure looks like
y = 122 + 49.99(x-1)
To write an equation in the form of y = c + d(x - 1) to represents Tariq's charging system:
Let's break down the problem.
We can see that the cost of the first hour of service is $122, the second hour is $171.99, and the third hour is $221.98.
Now, let's analyze the pattern. We can observe that the cost for each successive hour is increasing by $49.99. This increment is consistent throughout all additional hours of service.
Using this information, we can write the equation:
y = c + d(x - 1)
- y represents the total cost of service.
- x represents the number of hours of service.
- c represents the initial cost for the first hour of service.
- d represents the constant increment in cost per additional hour.
From the information given, we know that the cost for the first hour is $122, so c = 122.
We also figured out that the increase in cost per additional hour is $49.99, so d = 49.99.
Let's substitute these values into the equation:
y = 122 + 49.99(x - 1)
Simplifying the equation, we get:
y = 122 + 49.99x - 49.99
Combining like terms, we have:
y = 49.99x + 72.01
Therefore, the equation that represents this situation is y = 49.99x + 72.01.
To write the equation in the form of y = c + d(x - 1), we need to understand the key components of the situation:
- y represents the cost of the service.
- c is the initial cost, i.e., the cost of the first hour.
- d is the incremental cost, i.e., the difference in the cost between consecutive hours.
- x represents the number of hours of service.
The problem states that the first hour of service costs $122. This implies that the initial cost, c, is $122.
The second hour of service costs $171.99, which is $49.99 more than the first hour ($122 + $49.99). This means that each subsequent hour has an incremental cost, d, of $49.99.
Now, let's construct the equation using the given information:
y = c + d(x - 1)
Substituting the known values:
y = $122 + $49.99(x - 1)
Simplifying further:
y = $122 + $49.99x - $49.99
Combining like terms:
y = $49.99x + $72.01
Therefore, the equation in the form of y = c + d(x - 1) representing Tariq's charging system is y = $49.99x + $72.01.