Proportional Relationships

Question

Question 1
Last month, Lucy and Britney each read three books. The tables show the number of pages in each book and the time it took Lucy and Britney to read each book. Which of the tables, if any, represent a proportional relationship?
Responses
A Lucy's table represents a proportional relationship.Lucy's table represents a proportional relationship.
B Britney's table represents a proportional relationship.Britney's table represents a proportional relationship.
C Both Lucy's and Britney's tables represent a proportional relationship.Both Lucy's and Britney's tables represent a proportional relationship.
D Neither Lucy's nor Britney's tables represent a proportional relationship.

Answer 1

To determine if either Lucy's or Britney's tables represent proportional relationships, we need to check if the ratios of the number of pages to the time taken to read each book are constant for each individual.

A proportional relationship has the characteristic that the ratio of one quantity to another is constant. In this case, we need to see if the ratio of pages to time is the same for each book.

Let's analyze the two tables:

1. Lucy’s Table:

   • Book 1: x pages and y time
   • Book 2: a pages and b time
   • Book 3: c pages and d time

   We would calculate the ratios for Lucy's books:

   • Ratio for Book 1: \( \frac{x}{y} \)
   • Ratio for Book 2: \( \frac{a}{b} \)
   • Ratio for Book 3: \( \frac{c}{d} \)

   If \( \frac{x}{y} = \frac{a}{b} = \frac{c}{d} \), then Lucy's table represents a proportional relationship.

2. Britney’s Table:

   • Follow the same procedure for Britney’s books.

After analyzing the given ratios, you can determine if they are constant across all books for each person.

Since I don't have the actual numbers from the tables, you'll need to check if either Lucy's or Britney's ratios are equal.

Responses:

• If Lucy’s ratios are equal, then A.
• If Britney’s ratios are equal, then B.
• If both are equal, then C.
• If neither are equal, then D.

Without the specific values from the tables, I cannot definitively answer which response is correct. Please check the ratios in the tables to conclude.

Answer 2

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Answer 3

To determine which response is correct regarding whether Lucy's or Britney's tables represent a proportional relationship, we need to confirm whether the ratios of the number of pages to the time taken to read each book are constant for each individual.

Here’s the guideline to answer the question:

1. Identify the ratio (pages/time) for each book in Lucy's and Britney's tables.

2. Check for constancy:

   • If the ratio for all of Lucy's books is the same, then Lucy's table represents a proportional relationship.
   • If the ratio for all of Britney's books is the same, then Britney's table represents a proportional relationship.

3. Choose the appropriate response:

   • If only Lucy's ratios are constant, choose A.
   • If only Britney's ratios are constant, choose B.
   • If both are constant, choose C.
   • If neither are constant, choose D.

To give you the correct answer, I would need to see the actual numbers from Lucy's and Britney's tables for the pages and the time taken. If you provide those details, I can help you ascertain which response is correct!