Question
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
Answers
GPT-4o mini
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.
### 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?
GPT-4o mini
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**.
### 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**.