Question

the table shows how many shirts four garment factories made and how long it took to make them. the relationship between the number of shirts and the number of days required to make the shirts is proportional.
a fifth factory (factory e) can make shirts at the same rate as the first four factories. which table(s) could represent the production rate of factory e?

Explanation:

Step1: Calculate the rate of shirts per day for the first four factories

For factory A: $\frac{600}{2}=300$ shirts per day.
For factory B: $\frac{900}{3}=300$ shirts per day.
For factory C: $\frac{1200}{4}=300$ shirts per day.
For factory D: $\frac{1500}{5}=300$ shirts per day.
The rate is 300 shirts per day.

Step2: Check the rates for factory E in each table

For the table with 1 day and 300 shirts: $\frac{300}{1}=300$ shirts per day (matches the rate).
For the table with 6 days and 1800 shirts: $\frac{1800}{6}=300$ shirts per day (matches the rate).
For the table with 1 day and 400 shirts: $\frac{400}{1}=400
eq300$ (does not match).
For the table with 6 days and 2400 shirts: $\frac{2400}{6}=400
eq300$ (does not match).

Answer:

The tables with 1 day and 300 shirts, and 6 days and 1800 shirts could represent the production rate of factory E.