Question
Suppose that Conor’s total cost to see the movie is $18.40 What is the value of t to make that possible? t is 15%
Answers
GPT-4o mini
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:
1. Let \( C \) be the base cost of the movie ticket before tax or fees.
2. 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.
If \( t \) represents a tax or surcharge, we can set up the equation as follows:
1. Let \( C \) be the base cost of the movie ticket before tax or fees.
2. 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.