Ask a New Question
Menu

UPS charges seven dollars for their first pound and $.20 for each additional pound FedEx charges five dollars for the first time and $.30 for each additional pound how many additional pounds P will take for UPA and FedEx to cost the same

3 answers

To find how many additional pounds \( P \) it takes for UPS and FedEx to cost the same, we can set up equations for the total charges of both services based on the weight in pounds.

UPS Charges

For UPS:

  • The cost for the first pound is $7.
  • The cost for additional pounds is $0.20 per pound.
  • Therefore, for \( P \) additional pounds (where the total weight is \( 1 + P \)): \[ \text{Cost}_{UPS} = 7 + 0.20P \]

FedEx Charges

For FedEx:

  • The cost for the first pound is $5.
  • The cost for additional pounds is $0.30 per pound.
  • Therefore, for \( P \) additional pounds (where the total weight is \( 1 + P \)): \[ \text{Cost}_{FedEx} = 5 + 0.30P \]

Setting Up the Equation

To find the number of additional pounds where both costs are equal, we can set the two cost equations equal to each other: \[ 7 + 0.20P = 5 + 0.30P \]

Solving for \( P \)

  1. Subtract \( 0.20P \) from both sides: \[ 7 = 5 + 0.10P \]
  2. Subtract 5 from both sides: \[ 2 = 0.10P \]
  3. Divide both sides by 0.10: \[ P = \frac{2}{0.10} = 20 \]

Conclusion

It will take 20 additional pounds for UPS and FedEx to cost the same.

When the cost is the same what is the cost?

To find the cost when the two shipping options (UPS and FedEx) are the same, we can substitute \( P = 20 \) back into either cost equation.

Using the UPS Cost Equation

The cost for UPS is given by: \[ \text{Cost}_{UPS} = 7 + 0.20P \]

Substituting \( P = 20 \): \[ \text{Cost}_{UPS} = 7 + 0.20(20) = 7 + 4 = 11 \]

Using the FedEx Cost Equation

The cost for FedEx is given by: \[ \text{Cost}_{FedEx} = 5 + 0.30P \]

Substituting \( P = 20 \): \[ \text{Cost}_{FedEx} = 5 + 0.30(20) = 5 + 6 = 11 \]

Conclusion

When the cost is the same, the total cost for both UPS and FedEx is $11.