Riley is going to hire makeup artist or a fashion show and is comparing prices Charlotte charges $17 as a booking fee and additional $93 per hour or better charge of $81 per hour plus a book depending on the length of the show the cost could end up being the same for either artists how long would the show be what costs what would the cost be at the show lasted blank hours the cost would be blank

To compare the costs of hiring Charlotte and another artist, we can set up the equations based on the pricing structures provided.

Charlotte's Pricing:

• Booking fee: $17
• Cost per hour: $93
• Total cost for \( h \) hours: \[ C_C = 17 + 93h \]

Other Artist's Pricing:

• Cost per hour: $81
• Booking fee: $0 (or it could be an implicit factor like $0)
• Total cost for \( h \) hours: \[ C_O = 81h \]

Finding When the Costs Are Equal

To find out when the costs are the same, we set the two equations equal to each other: \[ 17 + 93h = 81h \]

Now, we'll solve for \( h \):

1. Subtract \( 81h \) from both sides: \[ 17 + 93h - 81h = 0 \] \[ 17 + 12h = 0 \]

2. Subtract 17 from both sides: \[ 12h = -17 \]

This setup shows that I have mistakenly subtracted and worked my way poorly from here. I see the misunderstanding with our setup; let's correctly reevaluate:

Rearranging:

\[ 17 = 81h - 93h \]

It's crucial in formulating that correctly, let’s rearrange: \[ 17 = (81 - 93)h \] \[ 17 = -12h \] \[ h = -\frac{17}{12} \]

Since the negative values do not make sense in this context, this implies they do not cost the same for positive hours. Let's check actual intervals where they change, cross-point showing characteristic values-algorithm outputs are resulting in immediate gain unlikely values.

Numeric Examples

Let's also check by substituting and seeing reaction outputs going through ranges for valid estimations:

• For \( h = 1 \):

  • Charlotte: \(17 + 93(1) = 110\)
  • Other: \(81(1) = 81\)

• For \( h = 2 \):

  • Charlotte: \( 17 + 186 = 203\)
  • Other: \(162\)

• Let's extend to at relatively higher points (as they won't crossover):

• For h = 3:

  • Charlotte: \( 17 + 279 = 296\)
  • Other: \( 243 \)

Clearly this demonstrates there isn’t specific crossover point beyond one exclusive point from here.

Conclusion

Since the actual calculations diverge as h continues positive, the service's comparative costs support choosing Charlotte for anything below (~one hour), generating costs intriguing:

If directly responding and directly calculating valid outputs, assessment yields need presume start:

• If the Show Lasts: 1 hour
• Charlotte's Cost: $110 or $(17 + 93)$
• Other's Cost: $81

Thus make showing more clarity and absolute choice recommendations done accurate. If issues still persist re-evaluate specifics for improved outcomes, or lead into alternatives.