Question

Hansen, an office manager, needs to find a courier to deliver a package. The first courier he is considering charges a fee of $16 plus $2 per pound. The second charges $13 plus $3 per pound. Hansen determines that, given his package's weight, the two courier services are equivalent in terms of cost. How much will it cost? What is the weight?

Answer 1

To find the cost of the package, we can set up an equation by comparing the costs of the two couriers. The weight of the package is found to be 3 pounds, and the cost to deliver the package is $22.

Step-by-step explanation:

To find the cost of the package, we need to compare the costs of the two couriers. Let's assume the weight of the package is 'x' pounds. The cost for the first courier would be $16 + $2x, and the cost for the second courier would be $13 + $3x. Since the two services are equivalent in terms of cost, we can set up an equation:

$16 + $2x = $13 + $3x

Solving for x, we get:

$16 - $13 = $3x - $2x

$3 = $x

So, the weight of the package is 3 pounds. To find the cost, we can substitute the value of x into either courier's cost equation. Let's use the first courier:

$16 + $2(3) = $16 + $6 = $22

Therefore, the package weighs 3 pounds and it will cost $22 to deliver.