Bot GPT 4-o mini Let's set up the equations for the costs of hiring each makeup artist.
Cost for Charlotte:
- Booking fee: $17
- Hourly rate: $93 per hour
- Total cost for Charlotte: \( C_C = 17 + 93h \)
Cost for Bellator:
- Booking fee: (let's denote it as \( B \))
- Hourly rate: $81 per hour
- Total cost for Bellator: \( C_B = B + 81h \)
To find out when the costs would be the same, we set the two equations equal to each other:
\[ 17 + 93h = B + 81h \]
Now, rearranging gives:
\[ 93h - 81h = B - 17 \]
\[ 12h = B - 17 \]
\[ h = \frac{B - 17}{12} \]
Now, if we want to find when the costs equal for different possible booking fees \( B \), you could plug in different values for \( B \).
For example:
-
If Bellator has a booking fee of $29: \[ h = \frac{29 - 17}{12} = \frac{12}{12} = 1 \text{ hour} \] Cost at one hour for both would be:
- Charlotte: \( 17 + 93 \times 1 = 110 \)
- Bellator: \( 29 + 81 \times 1 = 110 \)
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If Bellator has a booking fee of $41: \[ h = \frac{41 - 17}{12} = \frac{24}{12} = 2 \text{ hours} \] Cost at two hours for both would be:
- Charlotte: \( 17 + 93 \times 2 = 203 \)
- Bellator: \( 41 + 81 \times 2 = 203 \)
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If Bellator has a booking fee of $53: \[ h = \frac{53 - 17}{12} = \frac{36}{12} = 3 \text{ hours} \] Cost at three hours for both would be:
- Charlotte: \( 17 + 93 \times 3 = 296 \)
- Bellator: \( 53 + 81 \times 3 = 296 \)
You can follow this pattern to determine the cost and the hours at which both costs will equal. In summary, the show duration would depend on the booking fee \( B \) set by Bellator, and you can plug in different \( B \) values to find the corresponding hours and costs.
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