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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