1. **State the problem:** We know that 42 students own their instrument, which is 37.5% of the total number of students in the band. We need to find the total number of students. 2. **Formula used:** To find the total when a part and its percentage are known, use the formula: $$\text{Total} = \frac{\text{Part}}{\text{Percentage}}$$ where Percentage is in decimal form. 3. **Convert percentage to decimal:** $$37.5\% = \frac{37.5}{100} = 0.375$$ 4. **Apply the formula:** $$\text{Total} = \frac{42}{0.375}$$ 5. **Simplify the division:** $$\text{Total} = \frac{42}{\cancel{0.375}} \times \frac{1}{\cancel{0.375}} = 112$$ (Here, we show the cancellation conceptually, but since 0.375 is a decimal, we directly divide 42 by 0.375.) 6. **Calculate:** $$\text{Total} = 112$$ 7. **Interpretation:** There are 112 students in the band in total. **Final answer:** 112 students