Question

1. 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:
solve and show your work below:

Explanation:

Step1: Define cost functions

Let \( C_{UPS} \) be UPS's cost and \( C_{FedEx} \) be FedEx's cost. For UPS: first pound is $7, then \( (p - 1) \) additional pounds at $0.20 each. So \( C_{UPS}=7 + 0.20(p - 1) \). For FedEx: first pound is $5, then \( (p - 1) \) additional pounds at $0.30 each. So \( C_{FedEx}=5 + 0.30(p - 1) \). Set them equal: \( 7 + 0.20(p - 1)=5 + 0.30(p - 1) \).

Step2: Simplify the equation

Expand both sides: \( 7 + 0.20p - 0.20 = 5 + 0.30p - 0.30 \). Simplify: \( 6.8 + 0.20p = 4.7 + 0.30p \).

Step3: Solve for p

Subtract \( 0.20p \) and \( 4.7 \) from both sides: \( 6.8 - 4.7 = 0.30p - 0.20p \). So \( 2.1 = 0.10p \). Then \( p=\frac{2.1}{0.10}=21 \).

Answer:

21