Feb 14-11:59 pm The table shows the total number of U S. participants in four high school sports over several school years. In 2013-2014, 46 3\% of cross-country participants were girls. The number of girls who participated in cross-country increased by \( 16 \% \) from 2013-2014 to 2014-2015. What percent of 2014-2015 cross-country participants were girls? Click the icon to view the table of participants. About \( \square \) \% of 2014-2015 cross country participants were girls. (Round to the nearest tenth as needed.)

To solve the problem, we need to follow these steps: 1. **Extract known conditions:** - In the 2013-2014 school year, 46.3% of cross-country participants were girls. - The number of girls participating in cross-country increased by 16% from 2013-2014 to 2014-2015. 2. **Let’s denote:** - \( P_{2013} \): Total number of cross-country participants in 2013-2014. - \( G_{2013} \): Number of girls participating in cross-country in 2013-2014. - \( G_{2014} \): Number of girls participating in cross-country in 2014-2015. - \( P_{2014} \): Total number of cross-country participants in 2014-2015. 3. **Calculate the number of girls in 2013-2014:** \[ G_{2013} = 0.463 \times P_{2013} \] 4. **Calculate the number of girls in 2014-2015:** Since the number of girls increased by 16%, we have: \[ G_{2014} = G_{2013} + 0.16 \times G_{2013} = 1.16 \times G_{2013} \] Substituting \( G_{2013} \): \[ G_{2014} = 1.16 \times (0.463 \times P_{2013}) = 0.53768 \times P_{2013} \] 5. **Now, we need to find the percentage of girls in 2014-2015:** To find the percentage of girls in 2014-2015, we need the total number of participants in 2014-2015, \( P_{2014} \). However, since we don't have the exact value of \( P_{2014} \), we will assume it remains the same as \( P_{2013} \) for the sake of calculation. Thus: \[ \text{Percentage of girls in 2014-2015} = \left( \frac{G_{2014}}{P_{2014}} \right) \times 100 \] Substituting \( G_{2014} \): \[ \text{Percentage of girls in 2014-2015} = \left( \frac{0.53768 \times P_{2013}}{P_{2013}} \right) \times 100 = 53.768\% \] 6. **Rounding to the nearest tenth:** \[ \text{Percentage of girls in 2014-2015} \approx 53.8\% \] Thus, about \( 53.8 \% \) of 2014-2015 cross-country participants were girls.