Question

UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each additional pound. How many pounds, p, will it take for UPS and FedEx to cost the same? Write the equation that could be used to find when these two companies would cost the same. USE P AS YOUR VARIABLE. Use your equation to solve for the number of pounds. pounds

Answer 1

We can write the cost function for UPS and FedEx depending on p (pounds).

UPS charges $7 for the first pound, and $0.20 for each additional pound. That means that there is a fixed cost and then a variable cost for every pound exceeding the first pound.

We can write this as:

`C_{\text{ups}}=7+0.2(p-1)`

The same happens for FedEx, but with different fixed and variable cost for the extra pounds:

`C_{\text{FedEx}}=5+0.3(p-1)`

We can calculate how many pounds will it take for both to cost the same by making both cost equal and solving for p:

`\begin{gathered} C_{\text{ups}}=C_{\text{fedex}} \\ 7+0.2(p-1)=5+0.3(p-1) \\ 7-5=0.3(p-1)-0.2(p-1) \\ 2=0.1(p-1) \\ p-1=(2)/(0.1)=20 \\ p=20+1=21 \end{gathered}`

At p=21 pounds, both services cost the same.