A1 Car Share Inc. offers car sharing for a [tex]\[tex]$129[/tex] yearly fee plus [tex]\$[/tex]16 \text{ per hour}[/tex] for the use of its car share. What equation models the total cost for use of A1 Car Share?

A. [tex]t = 129 + 16h[/tex]
B. [tex]t = \frac{129}{16}[/tex]
C. [tex]t = 129h + 16[/tex]
D. None of the above



Answer :

Let's analyze each option step by step to determine which equation correctly models the total cost for using A1 Car Share.

1. Understanding the problem:
- There is a fixed yearly fee of [tex]$129. - In addition to the fixed fee, there is a charge of $[/tex]16 per hour for using the car.

2. Formulating the equation:
- We need an equation that takes into account both the fixed fee and the hourly charge.
- Let [tex]\( t \)[/tex] represent the total cost and [tex]\( h \)[/tex] represent the number of hours of car usage.

3. Option A: [tex]\( t = 129 + 16h \)[/tex]
- This equation suggests that the total cost [tex]\( t \)[/tex] is the sum of the fixed fee ([tex]$129) and the product of the hourly rate ($[/tex]16) and the number of hours ([tex]\( h \)[/tex]).
- This correctly incorporates both the fixed fee and the variable hourly cost.

4. Option B: [tex]\( t = \frac{129}{16} \)[/tex]
- This equation suggests that the total cost [tex]\( t \)[/tex] is the fixed fee divided by the hourly rate.
- This does not make sense in the context of the given problem since it does not account for the variable cost due to hours of usage.

5. Option C: [tex]\( t = 129h + 16 \)[/tex]
- This equation suggests that the fixed fee should be multiplied by the number of hours, and then $16 is added.
- This is incorrect because the fixed fee should not vary with the number of hours.

6. Conclusion:
- From the analysis, Option A ([tex]\( t = 129 + 16h \)[/tex]) correctly models the total cost for using A1 Car Share.
- Therefore, the correct answer is:

[tex]\[ \boxed{A} \][/tex]