1. **State the problem:** A photograph scale shows that every $1 \frac{1}{4}$ inches represents 100 yards in real life. The mountain height in the photo is 8 inches. Find the actual height of the mountains. 2. **Convert mixed number to improper fraction:** $$1 \frac{1}{4} = \frac{5}{4}$$ inches. 3. **Set up the proportion:** $$\frac{5}{4} \text{ inches} : 100 \text{ yards} = 8 \text{ inches} : x \text{ yards}$$ 4. **Write the equation:** $$\frac{5}{4} : 100 = 8 : x \implies \frac{5}{4} / 100 = 8 / x$$ 5. **Rewrite division as multiplication:** $$\frac{5}{4} \times \frac{1}{100} = \frac{8}{x}$$ 6. **Simplify left side:** $$\frac{5}{400} = \frac{8}{x}$$ 7. **Cross multiply:** $$5x = 8 \times 400$$ 8. **Calculate right side:** $$5x = 3200$$ 9. **Divide both sides by 5:** $$\cancel{5}x = \frac{3200}{\cancel{5}}$$ $$x = 640$$ 10. **Answer:** The actual height of the mountains is $640$ yards.