To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional po

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To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional pound. To ship a package with FedEx, the cost will be $5 for the first pound and $0.30 for each additional pound. How many pounds will it take for UPS and FedEx to cost the same? If you needed to ship a package that weighs 8 lbs, which shipping company would you choose and how much would you pay?

UPS: Set up the cost function C(p) where p is the number of pounds:
C(p) = Number of pounds over 1 * cost per pounds + first pound
C(p) = 0.2(p - 1) + 7

FedEx: Set up the cost function C(p) where p is the number of pounds:
C(p) = Number of pounds over 1 * cost per pounds + first pound
C(p) = 0.3(p - 1) + 5

When will the costs equal each other? Set the cost functions equal to each other:
0.2(p - 1) + 7 = 0.3(p - 1) + 5
0.2p - 0.2 + 7 = 0.3p - 0.3 + 5
0.2p + 6.8 = 0.3p + 4.7

To solve this equation for p, we type it in our search engine and we get:
p = 21
So at 21 pounds, both UPS and FedEx costs are equal

Now, find out which shipping company has a better rate at 8 pounds:

UPS:
C(8) = 0.2(8 - 1) + 7
C(8) = 0.2(7) + 7
C(8) = 1.4 + 7
C(8) = 8.4

FedEx:
C(8) = 0.3(8 - 1) + 5
C(8) = 0.3(7) + 5
C(8) = 2.1 + 5
C(8) = 7.1

Therefore, FedEx is the better cost at 8 pounds since the cost is lower