To determine who had a greater ratio of darts that popped balloons to total darts, we need to calculate the ratio for both Cassie and Molly.
First, let's calculate Cassie's ratio:
- Cassie popped 7 balloons with 10 darts thrown. Therefore, the ratio of darts that popped balloons to total darts for Cassie is:
\[ \text{Cassie's ratio} = \frac{7}{10} \]
Next, let's calculate Molly's ratio:
- Molly popped 4 balloons with 5 darts thrown. Therefore, the ratio of darts that popped balloons to total darts for Molly is:
\[ \text{Molly's ratio} = \frac{4}{5} \]
Now we need to compare the two ratios, \( \frac{7}{10} \) and \( \frac{4}{5} \).
To compare these fractions, we can convert them to a common denominator. The least common multiple of the denominators \(10\) and \(5\) is \(10\).
Now, we convert Molly's ratio to have a denominator of \(10\):
\[ \frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10} \]
Now we compare:
- Cassie's ratio: \( \frac{7}{10} \)
- Molly's ratio: \( \frac{8}{10} \)
Since \( \frac{8}{10} > \frac{7}{10} \), we find that:
\[ \text{Molly's ratio} > \text{Cassie's ratio} \]
Thus, Molly had a greater ratio of darts that popped balloons to total darts.
The answer is: Molly had a greater ratio.
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