Question

which company has shipping rates that represent a proportional relationship? explain.
company a
weight (lb) total cost ($)
1 10.55
2 10.85
3 11.15
company b
weight (lb) total cost ($)
1 2.75
2 5.50
3 8.25
choose... ; the ratios of cost to weight are choose...

Explanation:

Step1: Recall proportional relationship

A proportional relationship has a constant ratio of \( \frac{\text{Total Cost}}{\text{Weight}} \) (i.e., \( y = kx \) where \( k \) is constant). We calculate this ratio for each company.

Step2: Calculate ratios for Company A

• For weight = 1 lb: \( \frac{10.55}{1}=10.55 \)
• For weight = 2 lb: \( \frac{10.85}{2} = 5.425 \)
• For weight = 3 lb: \( \frac{11.15}{3}\approx3.717 \)

The ratios are not constant.

Step3: Calculate ratios for Company B

• For weight = 1 lb: \( \frac{2.75}{1}=2.75 \)
• For weight = 2 lb: \( \frac{5.50}{2}=2.75 \)
• For weight = 3 lb: \( \frac{8.25}{3}=2.75 \)

The ratios are constant (\( 2.75 \)).

Answer:

Company B; the ratios of cost to weight are constant (2.75 for all weights), while Company A's ratios vary. So Company B has a proportional relationship.