To determine how much it will cost to take multiple rides on a train, where each individual ride costs [tex]$\$[/tex] 3.40[tex]$, we need to come up with a mathematical model to express this relationship.
Let's break it down step-by-step:
1. Identify the variables:
- Let \( C \) represent the total cost in dollars.
- Let \( x \) represent the number of rides.
2. Understand the cost per ride:
- Each ride on the train costs $[/tex]\[tex]$ 3.40$[/tex].
3. Formulate the model:
- To find the total cost [tex]\( C \)[/tex] for [tex]\( x \)[/tex] rides, we multiply the cost per ride by the number of rides.
- Thus, [tex]\( C = 3.40 \times x \)[/tex].
This model, [tex]\( C = 3.40x \)[/tex], shows that the total cost [tex]\( C \)[/tex] is directly proportional to the number of rides [tex]\( x \)[/tex]. Each additional ride simply adds an additional [tex]$\$[/tex] 3.40[tex]$ to the total cost.
Now let’s look at the given options:
a. \( C = 3.40x \) ⟵ Correct
b. \( Cx = 3.40 \) ⟵ Incorrect (this would imply that \( C \) and \( x \) somehow multiply to a constant $[/tex]\[tex]$ 3.40$[/tex], which is not true)
c. [tex]\( C = 3.40 + x \)[/tex] ⟵ Incorrect (this suggests that the total cost is the sum of [tex]$\$[/tex] 3.40$ and the number of rides, which is not the intended model)
d. [tex]\( C = 3.40 - x \)[/tex] ⟵ Incorrect (this indicates the cost decreases as the number of rides increases, which does not make sense in this context)
Hence, the correct answer is:
a. [tex]\( C = 3.40x \)[/tex]
