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

Answer 1

It will take 21 pounds for UPS and FedEx to cost the same

Step-by-step explanation:

There are two options

1. UPS charges 7$ for the first pound, and $0.20 for each

   additional pound

2. FedEx charges 5$ for the first pound and $0.30 for each

    additional pound

We need to find for how many pounds "p" it will take for UPS and

FedEx to cost the same

∵ P is the number of pounds

∴ The number of pounds after the first pound = p - 1

In UPS

∵ The cost of the first pound is $7

∵ The cost of each additional pound is $0.2

∴ The cost in UPS = 7 + 0.2(p - 1)

- Simplify it

∴ The cost in UPS = 7 + 0.2(p) + 0.2(-1)

∴ The cost in UPS = 7 + 0.2p - 0.2

∴ The cost in UPS = 0.2p + 6.8 ⇒ (1)

In FedEX

∵ The cost of the first pound is $5

∵ The cost of each additional pound is $0.3

∴ The cost in FedEX = 5 + 0.3(p - 1)

- Simplify it

∴ The cost in FedEX = 5 + 0.3(p) + 0.3(-1)

∴ The cost in FedEX = 5 + 0.3p - 0.3

∴ The cost in FedEX = 0.3p + 4.7 ⇒ (2)

Equate (1) and (2) ⇒ the costs of the two options

∵ 0.2p + 6.8 = 0.3p + 4.7

- Subtract 0.2p from both sides

∴ 6.8 = 0.1p + 4.7

- Subtract 4.7 from both sides

∴ 2.1 = 0.1p

- Divide both sides by 0.1

∴ p = 21 pounds

It will take 21 pounds for UPS and FedEx to cost the same

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