A cab ride costs $10 to get into the cab and then $4 per mile. Change this to proportional.
Let x represent the number of miles traveled.
The cost to get into the cab is $10 and the cost per mile is $4.
The total cost of the cab ride is therefore $10 + $4x.
To change this to a proportional equation, we need to determine a constant rate per mile that can be multiplied by the number of miles traveled.
Let's call the cost per mile "p" (in dollars per mile).
To get into the cab, the cost is $10, which is the base fare.
So, the cost of the cab ride can be represented by the equation:
Cost = $10 + (p × miles)
Since the charge for the base fare ($10) does not depend on the number of miles traveled, it remains constant.
Therefore, the proportional equation for the cab ride would be:
Cost = $10 + (p × miles)
To change the given cab ride cost to a proportional relationship, we need to identify the constant of proportionality.
Let's assume the number of miles traveled is represented by x, and C(x) represents the total cost.
According to the given information:
- The initial cost to get into the cab is $10, which is a fixed cost regardless of the distance traveled.
- The cost per mile is $4, which is the constant charge for each mile traveled.
Thus, our proportional relationship for the cost of the cab ride can be represented as:
C(x) = 10 + 4x
In this equation:
- 10 is the constant term, which represents the initial fixed cost to enter the cab.
- 4 is the coefficient of x, which represents the charge per mile traveled.
- x represents the number of miles traveled. The value of x will vary depending on the distance covered.
Therefore, to find the cost of the cab ride for a specific number of miles, you can substitute the value of x into the equation C(x) = 10 + 4x.