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.)

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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.
About $$ 53.8 \% $$ of 2014-2015 cross-country participants were girls.

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