To determine the value of \( t \) that allows for a total cost of $18.40, given that \( t \) is 15%, we need to understand in what context \( t \) is being applied.
If \( t \) represents a tax or surcharge, we can set up the equation as follows:
- Let \( C \) be the base cost of the movie ticket before tax or fees.
- The total cost after applying a percentage \( t \) (which is 15% or 0.15) to the base cost will be:
\[ \text{Total Cost} = C + (t \times C) \]
This can be rewritten as:
\[ \text{Total Cost} = C(1 + t) \]
Substituting \( t = 0.15 \):
\[ \text{Total Cost} = C(1 + 0.15) = C \times 1.15 \]
Given that the total cost is $18.40, we can set up the equation:
\[ C \times 1.15 = 18.40 \]
To find \( C \):
\[ C = \frac{18.40}{1.15} \]
Calculating this gives:
\[ C \approx 16.00 \]
Thus, if the base cost of the movie ticket is approximately $16.00, then applying 15% to this value will yield a total cost of $18.40.
In summary, the value of \( t \) (0.15 or 15%) is correctly applied, and the base cost \( C \) must be approximately $16.00 to achieve the total cost of $18.40.
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