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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. Ted charges for showing up, plus per hour. Levi charges plus 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 _____.
Full solution
Q. 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. Ted charges for showing up, plus per hour. Levi charges plus 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 _____.
- Define Variables: Let's define the variables:Let be the number of hours the photo shoot lasts.Let be the total cost for hiring either stylist.Ted's cost: Levi's cost:
- Write Equations: Now we write the system of equations based on the information given:For Ted: For Levi:
- Set Equations Equal: Since the costs are the same, we can set the equations equal to each other to find the duration of the photo shoot:
- Solve for x: Now we solve for x:
- Substitute Back: Now that we have the value of , we can substitute it back into either equation to find the total cost . We'll use Ted's equation:
- Final Results: We have found the duration and the cost:Duration: hourCost: If the shoot lasted for hour, either stylist would cost .
