Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. A fashion photographer needs to hire a stylist to prepare his models. Michelle charges $189 for showing up, plus $73 per hour. Vince charges $186 plus $74 per hour. The photographer realizes that, given the expected duration of his photo shoot, either stylist would cost him the same amount. What would the duration be? What would the cost be? If the shoot lasted for _____ hours, either stylist would cost $_____.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  A fashion photographer needs to hire a stylist to prepare his models. Michelle charges $189 for showing up, plus $73 per hour. Vince charges $186 plus $74 per hour. The photographer realizes that, given the expected duration of his photo shoot, either stylist would cost him the same amount. What would the duration be? What would the cost be?   If the shoot lasted for _____ hours, either stylist would cost $_____.

Bytelearn · Accepted Answer

Define Costs and Duration: Let's define the total cost for hiring Michelle as M and the total cost for hiring Vince as V. Let's also define the duration of the photo shoot in hours as h. According to the problem, Michelle charges $189 for showing up plus $73 per hour, so her total cost can be represented by the equation: M = 73h + 189Michelle's Cost Equation: Similarly, Vince charges $186 for showing up plus $74 per hour, so his total cost can be represented by the equation: V = 74h + 186Vince's Cost Equation: The photographer realizes that the cost for either stylist would be the same, so we can set the two equations equal to each other to find the duration of the photo shoot: 73h + 189 = 74h + 186Set Equations Equal: To solve for h, we will subtract 73h from both sides of the equation: 73h + 189 - 73h = 74h + 186 - 73h This simplifies to: 189 = h + 186Solve for Duration: Now, we subtract 186 from both sides of the equation to solve for h: 189 - 186 = h + 186 - 186 This simplifies to: 3 = hSubstitute Duration: Now that we have the duration h, we can find the total cost for either stylist by substituting h back into one of the original equations. Let's use Michelle's equation: M = 73h + 189 M = 73(3) + 189Calculate Total Cost: Now we perform the calculation: M = 219 + 189 M = 408Final Results: We have found that the duration of the photo shoot is 3 hours and the total cost for either stylist is $408.

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