2 Tables. A 2-column table with 2 rows is titled Table A. Column 1 is labeled Squares with entries 5, 10. Column 2 is labeled Circles with entries 3, 6. A 2-column table with 2 rows is titled Table B. Column 1 is labeled Squares with entries 10, 20. Column 2 is labeled Circles with entries 3, 9.

Question

Which statement is true about the ratios of squares to circles in the tables?
The ratios in Table A are greater than the ratios in Table B.
The ratios in Table B are greater than the ratios in Table A.
Only some of the ratios in Table A are greater than the ratios in Table B.
The ratios in Table A are equal to the ratios in Table B.

Answer 1

To compare the ratios of squares to circles in both tables, let's calculate the ratios for each row in Table A and Table B.

Table A:

• For the first row:

  • Squares: 5
  • Circles: 3
  • Ratio (Squares to Circles) = 5/3 ≈ 1.67

• For the second row:

  • Squares: 10
  • Circles: 6
  • Ratio (Squares to Circles) = 10/6 = 5/3 ≈ 1.67

Table B:

• For the first row:

  • Squares: 10
  • Circles: 3
  • Ratio (Squares to Circles) = 10/3 ≈ 3.33

• For the second row:

  • Squares: 20
  • Circles: 9
  • Ratio (Squares to Circles) = 20/9 ≈ 2.22

Now we can compare the ratios:

• Table A ratios: 5/3 (≈ 1.67) for both rows.
• Table B ratios: 10/3 (≈ 3.33) for the first row and 20/9 (≈ 2.22) for the second row.

Now let's summarize the comparisons:

• 5/3 (≈ 1.67) from Table A is less than 10/3 (≈ 3.33) from Table B.
• 5/3 (≈ 1.67) from Table A is also less than 20/9 (≈ 2.22) from Table B.

Based on the calculations, all ratios in Table A are less than the ratios in Table B.

Thus, the true statement is: The ratios in Table B are greater than the ratios in Table A.