The number of days required to make shirts is proportional, as shown in the table below:
| Factory | Number of Days | Number of Shirts |
|---|---|---|
| A | 2 | 600 |
| B | 3 | 900 |
| C | 4 | 1200 |
| D | 5 | 1500 |
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?
| Factory | Number of Days | Number of Shirts |
|---|---|---|
| E | 1 | 400 |
| Factory | Number of Days | Number of Shirts |
|---|---|---|
| E | 1 | 300 |
| Factory | Number of Days | Number of Shirts |
|---|---|---|
| E | 6 | 1,800 |
Answer (2)
Tables 2 and 3 could represent the production rate of Factory E as they both match the production rate of 300 shirts/day. Table 1, however, does not match. Thus, the correct options are Tables 2 and 3.
;
Calculate the production rate for factories A, B, C, and D: Number of Days Number of Shirts = 300 shirts/day.
Calculate the production rate for each Factory E table.
Table 2 and Table 3 have a production rate of 300 shirts/day.
Tables 2 and 3 could represent the production rate of Factory E: $\boxed{\text{Tables 2 and 3}}.
Explanation
Understanding the Problem We are given a table showing the number of days and shirts produced by four factories (A, B, C, and D). We are told that the number of days required to make the shirts is proportional, meaning the rate of shirt production is constant across all factories. We need to determine which of the provided tables for Factory E could represent its production rate, given that Factory E produces shirts at the same rate as the other factories.
Calculating Production Rates First, let's calculate the production rate (shirts per day) for factories A, B, C, and D. The production rate is calculated as the number of shirts divided by the number of days.
Determining the Common Production Rate Factory A: Rate = 2 600 = 300 shirts/day Factory B: Rate = 3 900 = 300 shirts/day Factory C: Rate = 4 1200 = 300 shirts/day Factory D: Rate = 5 1500 = 300 shirts/day
The production rate for all four factories is 300 shirts/day.
Checking Factory E Tables Now, let's examine each table for Factory E and calculate its production rate to see if it matches the rate of 300 shirts/day.
Table 1: Rate = 1 400 = 400 shirts/day. This rate does not match the common rate. Table 2: Rate = 1 300 = 300 shirts/day. This rate matches the common rate. Table 3: Rate = 6 1800 = 300 shirts/day. This rate matches the common rate.
Conclusion Therefore, tables 2 and 3 could represent the production rate of Factory E, as they both have a production rate of 300 shirts/day, which is the same as factories A, B, C, and D.
Examples
Understanding proportional relationships is crucial in many real-world scenarios. For example, if you are baking a cake and need to double the recipe, you need to ensure that all ingredients are increased proportionally to maintain the cake's consistency and taste. Similarly, in manufacturing, maintaining proportional production rates ensures consistent output and efficient resource allocation. This concept is also vital in understanding currency exchange rates, where the value of one currency is proportional to another.
