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Sean, an office manager, needs to find a courier to deliver a package. The first courier he is considering charges a fee of plus per pound. The second charges plus per pound.Sean determines that, given his package's weight, the two courier services are equivalent in terms of cost. How much will it cost to deliver the package? How much does Sean's package weigh?It will cost ____ to deliver Sean's package using either courier service. The package weighs ____ pounds.
Full solution
Q. Sean, an office manager, needs to find a courier to deliver a package. The first courier he is considering charges a fee of plus per pound. The second charges plus per pound.Sean determines that, given his package's weight, the two courier services are equivalent in terms of cost. How much will it cost to deliver the package? How much does Sean's package weigh?It will cost ____ to deliver Sean's package using either courier service. The package weighs ____ pounds.
- Cost Equation for First Courier: Equation for the first courier: Total cost = + per pound. Let the weight of the package be pounds. Then, the cost equation is .
- Cost Equation for Second Courier: Equation for the second courier: Total cost = + per pound. Using the same variable for weight, the cost equation is .
- Set Equations Equal: Set the two equations equal to find the weight where the costs are the same: .
- Solve for Weight: Solve for : Subtract from both sides to get ; then subtract from both sides to get .
- Find Weight: Divide both sides by to find : pounds.
- Substitute to Find Cost: Substitute back into either courier's cost equation to find the cost: Using the first courier's equation, dollars.
