1. **State the problem:** We need to find the total number of spectators at a soccer match given that 60% are men, the rest are women and children, the number of children is \(\frac{2}{3}\) of the number of women, and there are 252 more men than women. 2. **Define variables:** Let the total number of spectators be \(T\). - Number of men = \(0.6T\) - Number of women = \(w\) - Number of children = \(\frac{2}{3}w\) 3. **Express the total:** Since men, women, and children make up all spectators, $$0.6T + w + \frac{2}{3}w = T$$ 4. **Combine like terms:** $$0.6T + \frac{5}{3}w = T$$ 5. **Rearrange to isolate \(w\):** $$\frac{5}{3}w = T - 0.6T = 0.4T$$ $$w = \frac{0.4T \times 3}{5} = 0.24T$$ 6. **Use the difference between men and women:** $$0.6T - w = 252$$ Substitute \(w = 0.24T\): $$0.6T - 0.24T = 252$$ $$0.36T = 252$$ 7. **Solve for \(T\):** $$T = \frac{252}{0.36} = 700$$ **Final answer:** There are \(700\) spectators altogether.