Question

Select the table that represents the ratio of white pentagons to red pentagons.



A.
White 21 33 39 57
Red 28 44 52 76

B.
White 23 33 39 57
Red 28 44 52 76

C.
White 21 44 39 57
Red 28 33 52 76

D.
White 20 33 39 57
Red 28 44 52 76

Answer 1

To determine which table represents the ratio of white pentagons to red pentagons, we must look at the values in each table and compute the ratio for each corresponding column.

The ratio is calculated as:
\[
\text{Ratio} = \frac{\text{Number of White Pentagons}}{\text{Number of Red Pentagons}}
\]

Let's calculate the ratios for each table:

**A.**
- \( \frac{21}{28} = \frac{3}{4} \)
- \( \frac{33}{44} = \frac{3}{4} \)
- \( \frac{39}{52} = \frac{3}{4} \)
- \( \frac{57}{76} \) (not simplified yet)

**B.**
- \( \frac{23}{28} \) (not simplified yet)
- \( \frac{33}{44} = \frac{3}{4} \)
- \( \frac{39}{52} = \frac{3}{4} \)
- \( \frac{57}{76} \) (not simplified yet)

**C.**
- \( \frac{21}{28} = \frac{3}{4} \)
- \( \frac{44}{33} \) (not simplified yet)
- \( \frac{39}{52} = \frac{3}{4} \)
- \( \frac{57}{76} \) (not simplified yet)

**D.**
- \( \frac{20}{28} = \frac{5}{7} \)
- \( \frac{33}{44} = \frac{3}{4} \)
- \( \frac{39}{52} = \frac{3}{4} \)
- \( \frac{57}{76} \) (not simplified yet)

Now, noticing that two of the tables yield the ratio \(\frac{3}{4}\) for most columns:

- **Table A**: Consistent \(\frac{3}{4}\) ratio for most columns.
- **Table B**: Shows variation starting from \(23/28\) but has \(\frac{3}{4}\) for some columns.
- **Table C**: Also inconsistent with a different value \(44/33\).
- **Table D**: Seems to have a different ratio altogether starting with \(\frac{5}{7}\).

After analyzing the results, it is clear that **Table A** maintains a consistent ratio of \(\frac{3}{4}\) across multiple columns, making it the best representation of the ratio of white pentagons to red pentagons.

Thus, the answer is **A**.