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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineMelissa is going to hire a makeup artist for a fashion show and is comparing prices. Sanjay charges $92\$92 as a booking fee and an additional $53\$53 per hour. Denise charges $52\$52 per hour, plus a booking fee of $95\$95. Depending on the length of the show, the cost could end up being the same for either artist. How long would the show be? What would the cost be?\newlineIf the show lasted for _____ hours, the cost would always be $\$_____.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineMelissa is going to hire a makeup artist for a fashion show and is comparing prices. Sanjay charges $92\$92 as a booking fee and an additional $53\$53 per hour. Denise charges $52\$52 per hour, plus a booking fee of $95\$95. Depending on the length of the show, the cost could end up being the same for either artist. How long would the show be? What would the cost be?\newlineIf the show lasted for _____ hours, the cost would always be $\$_____.
  1. Define Variables: Let's define the variables:\newlineLet xx represent the number of hours the show lasts.\newlineLet CC represent the total cost for hiring either makeup artist.
  2. Write Equations: We can write two equations to represent the cost for each makeup artist:\newlineFor Sanjay: C=92+53xC = 92 + 53x\newlineFor Denise: C=95+52xC = 95 + 52x
  3. Set Equations Equal: To find when the costs are the same, we set the two equations equal to each other:\newline92+53x=95+52x92 + 53x = 95 + 52x
  4. Solve for x: Now, we solve for x by subtracting 52x52x from both sides of the equation:\newline92+53x−52x=95+52x−52x92 + 53x - 52x = 95 + 52x - 52x\newline92+x=9592 + x = 95
  5. Substitute xx: Next, we subtract 9292 from both sides to solve for xx:92+x−92=95−9292 + x - 92 = 95 - 92x=3x = 3
  6. Calculate Total Cost: Now that we have the value for xx, we can substitute it back into either of the original equations to find the cost CC. We'll use Sanjay's equation:\newlineC=92+53(3)C = 92 + 53(3)
  7. Calculate Total Cost: Now that we have the value for xx, we can substitute it back into either of the original equations to find the cost CC. We'll use Sanjay's equation:\newlineC=92+53(3)C = 92 + 53(3) Calculate the total cost:\newlineC=92+159C = 92 + 159\newlineC=251C = 251

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