1. **State the problem:** We have two types of yearbooks: pre-ordered at 38 each and normal at 45 each. There are 24 students in total who spent 975 in total. We need to find how many students pre-ordered the yearbook. 2. **Define variables:** Let $x$ be the number of pre-ordered yearbooks. 3. **Write the equation:** The number of normal yearbooks is $24 - x$. The total cost equation is: $$38x + 45(24 - x) = 975$$ 4. **Simplify the equation:** $$38x + 1080 - 45x = 975$$ $$-7x + 1080 = 975$$ 5. **Solve for $x$:** $$-7x = 975 - 1080$$ $$-7x = -105$$ $$x = \frac{-105}{-7} = 15$$ 6. **Interpret the result:** 15 students pre-ordered the yearbook. **Final answer:** 15 students pre-ordered the yearbook.