Final answer:
To ship a package, UPS charges $7 for the first pound and $0.20 for each additional pound, while FedEx charges $5 for the first pound and $0.30 for each additional pound. To find when the costs are the same, we can set up an equation and solve for the number of pounds. It will take 20 pounds for UPS and FedEx to cost the same, and the cost will be $10.80.
Step-by-step explanation:
To determine the number of pounds, p, it will take for UPS and FedEx to cost the same, we can set up an equation.
For UPS, the cost is $7 for the first pound, and $0.20 for each additional pound.
For FedEx, the cost is $5 for the first pound, and $0.30 for each additional pound.
We can set up the equation: $7 + $0.20(p-1) = $5 + $0.30(p-1).
Simplifying the equation, we get $2 + $0.20p - $0.20 = $0.30p - $0.30.
Combining like terms, we have $0.20p - $0.30p = $2 - $0.20 + $0.30.
Simplifying further, we get $-0.10p = $2 + $0.10.
Dividing both sides by $-0.10, we find that p = 20.
Therefore, it will take 20 pounds for UPS and FedEx to cost the same.
To determine the cost of shipping, we can substitute p = 20 into either of the original cost equations.
If we use UPS: $7 + $0.20(20 - 1) = $7 + $0.20(19) = $7 + $3.80 = $10.80.
Therefore, the cost will be $10.80 when shipping 20 pounds using either UPS or FedEx.