Sean, an office manager, needs to find a courier to deliver a package. The first courier he is considering charges a fee of $20 plus $1 per pound. The second charges $8 plus $3 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.

Question

Sean, an office manager, needs to find a courier to deliver a package. The first courier he is considering charges a fee of $20 plus $1 per pound. The second charges $8 plus $3 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.

Bytelearn · Accepted Answer

Cost Equation for First Courier:  Equation for the first courier: Total cost = $20 + $1 per pound. Let the weight of the package be w pounds. Then, the cost equation is C = 1w + 20. Cost Equation for Second Courier:  Equation for the second courier: Total cost = $8 + $3 per pound. Using the same variable w for weight, the cost equation is C = 3w + 8. Set Equations Equal:  Set the two equations equal to find the weight w where the costs are the same: 1w + 20 = 3w + 8. Solve for Weight:  Solve for w: Subtract 1w from both sides to get 20 = 2w + 8; then subtract 8 from both sides to get 12 = 2w. Find Weight:  Divide both sides by 2 to find w: w = 12 / 2 = 6 pounds. Substitute to Find Cost:  Substitute w back into either courier's cost equation to find the cost: Using the first courier's equation, C = 1(6) + 20 = 6 + 20 = 26 dollars.

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