To determine which crown had a greater ratio of red gems to purple gems, we need to calculate the ratio for both crowns.
King's Crown:
- Red gems = 5
- Purple gems = 8
The ratio of red to purple gems for the king's crown is: \[ \text{Ratio for King's Crown} = \frac{5 \text{ red gems}}{8 \text{ purple gems}} = \frac{5}{8} \]
Prince's Crown:
- Red gems = 4
- Purple gems = 5
The ratio of red to purple gems for the prince's crown is: \[ \text{Ratio for Prince's Crown} = \frac{4 \text{ red gems}}{5 \text{ purple gems}} = \frac{4}{5} \]
Now, let's compare the two ratios:
- King's Crown: \( \frac{5}{8} \)
- Prince's Crown: \( \frac{4}{5} \)
To compare these ratios, we can convert them to a common denominator or compare their decimal values:
- \( \frac{5}{8} = 0.625 \)
- \( \frac{4}{5} = 0.8 \)
Since \( 0.8 > 0.625 \), the prince's crown has the greater ratio of red gems to purple gems.
Therefore, the answer is: B. The prince's crown had the greater ratio.
1 answer