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 her models. Lacey charges $201 for showing up, plus $71 per hour. Cindy charges $198 plus $74 per hour. The photographer realizes that, given the expected duration of her photo shoot, either stylist would cost her 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 her models. Lacey charges $201 for showing up, plus $71 per hour. Cindy charges $198 plus $74 per hour. The photographer realizes that, given the expected duration of her photo shoot, either stylist would cost her 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

Stylist Cost Equations: Let x represent the duration of the photo shoot in hours, and y represent the total cost for hiring a stylist. For Lacey: Base charge: $201 Hourly rate: $71 Equation based on the given information: Total cost y = base charge + (hourly rate * duration x) y = 71x + 201 For Lacey, the equation is: y = 71x + 201System of Equations: For Cindy: Base charge: $198 Hourly rate: $74 Equation based on the given information: Total cost y = base charge + (hourly rate * duration x) y = 74x + 198 For Cindy, the equation is: y = 74x + 198Solving for Duration: System of equations: y = 71x + 201 y = 74x + 198 To find the duration x when the cost y is the same for both stylists, set the two equations equal to each other: 71x + 201 = 74x + 198Substitute and Calculate: Solve for x by isolating the variable. Subtract 71x from both sides of the equation: 71x + 201 - 71x = 74x + 198 - 71x 201 = 3x + 198 Now, subtract 198 from both sides: 201 - 198 = 3x + 198 - 198 3 = 3xFinal Result: Divide both sides by 3 to solve for x: 3/3 = (3x)/3 1 = x So, x = 1Now that we have x = 1, we can find the total cost y by substituting x into one of the original equations. Substitute 1 for x in y = 71x + 201: y = 71(1) + 201 y = 71 + 201 y = 272 So, y = 272We have found that the duration x is 1 hour and the total cost y is $272. Therefore, if the shoot lasted for 1 hour, either stylist would cost $272.

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