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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Kira, an office manager, needs to find a courier to deliver a package. The first courier she is considering charges a fee of plus per kilogram. The second charges plus per kilogram. Kira determines that, given her package's weight, the two courier services are equivalent in terms of cost. What is the weight? How much will it cost?At a package weight of kilograms, the two couriers both cost .
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Kira, an office manager, needs to find a courier to deliver a package. The first courier she is considering charges a fee of plus per kilogram. The second charges plus per kilogram. Kira determines that, given her package's weight, the two courier services are equivalent in terms of cost. What is the weight? How much will it cost?At a package weight of kilograms, the two couriers both cost .
- Define Weight and Costs: Let's denote the weight of the package as ' extit{w}' kilograms. The cost for the first courier is plus per kilogram, and the cost for the second courier is plus per kilogram. We can write two equations to represent the costs for each courier.First courier: Cost = Second courier: Cost = Since the costs are equivalent, we can set these two expressions equal to each other to find the weight '\textit{w}'.
- Set Equation for Costs: Set up the equation based on the costs being equal.
- Solve for Weight: Solve for by rearranging the equation.Subtract from both sides:Subtract from both sides:
- Calculate Cost for First Courier: Now that we have the weight of the package, we can find out how much it will cost for either courier.Using the first courier's cost equation:Cost = Cost = Cost = Cost =
- Check Cost with Second Courier: To ensure we did not make a mistake, we can check the cost with the second courier's cost equation.
