Answer: To find the weight at which a customer would pay the same amount with either Postal Mile or Packages-R-Us, we can set up an equation based on their respective pricing structures.
Let's represent the weight of the package in pounds as "W."
For Postal Mile, the cost is $7.20 for the first pound and 45 cents for each additional pound. So, the cost with Postal Mile is given by:
Cost with Postal Mile = $7.20 + ($0.45 * (W - 1))
For Packages-R-Us, the cost is $9 for the first pound and 2 cents for each additional pound. So, the cost with Packages-R-Us is given by:
Cost with Packages-R-Us = $9 + ($0.02 * (W - 1))
Now, we want to find the weight "W" at which the costs are the same for both companies. Therefore, we can set up the following equation:
$7.20 + ($0.45 * (W - 1)) = $9 + ($0.02 * (W - 1))
Now, let's solve this equation for "W":
$7.20 + $0.45W - $0.45 = $9 + $0.02W - $0.02
Next, let's simplify the equation:
$7.20 - $0.45 = $9 - $0.02 + $0.45W - $0.02W
$6.75 = $8.98 + $0.43W - $0.02W
Now, subtract $8.98 from both sides:
$6.75 - $8.98 = $0.43W - $0.02W
-$2.23 = $0.41W
Now, divide both sides by $0.41 to solve for "W":
W = -$2.23 / $0.41 ≈ -5.44
Since the weight of a package cannot be negative, this means that there is no positive weight at which the costs are the same for both companies. In other words, a customer will never pay the same amount with either company, as Postal Mile's pricing is different from Packages-R-Us, and the cost will always differ based on the weight of the package.
Explanation: