In a college band, the ratio of brass to woodwind players is \( 13: 9 \). If there are 243 woodwind players iow many total students are there?

To determine the total number of students in the college band, follow these steps: 1. **Understand the Ratio:** - The ratio of brass to woodwind players is \( 13:9 \). - This means for every 13 brass players, there are 9 woodwind players. 2. **Determine the Value of One Part:** - You're given that there are 243 woodwind players, which corresponds to the "9 parts" in the ratio. - To find the value of one part: \[ \text{Value of one part} = \frac{243 \text{ woodwind players}}{9 \text{ parts}} = 27 \text{ players per part} \] 3. **Calculate the Number of Brass Players:** - Since there are 13 parts for brass players: \[ \text{Brass players} = 13 \times 27 = 351 \text{ players} \] 4. **Find the Total Number of Students:** - Add the number of brass players to the number of woodwind players: \[ \text{Total students} = 351 \text{ brass} + 243 \text{ woodwind} = 594 \text{ students} \] **Answer:** There are a total of **594** students in the band.