1. **Stating the problem:** We have 100 people visiting a gym on Saturday. Among them, 18 attended the spinning class, 10 attended both spinning and circuits classes, and 56 did not attend either class. We want to represent this information on a Venn diagram. 2. **Understanding the sets:** Let $S$ be the set of people attending the spinning class and $C$ be the set attending the circuits class. 3. **Given data:** - Total people: $100$ - $|S| = 18$ - $|S \cap C| = 10$ - People who did not attend either class: $56$ 4. **Find the number attending only spinning:** $$\text{Spinning only} = |S| - |S \cap C| = 18 - 10 = 8$$ 5. **Find the number attending only circuits:** Let $x$ be the number attending only circuits. 6. **Use total to find $x$:** Total = (Spinning only) + (Both classes) + (Circuits only) + (Neither) $$100 = 8 + 10 + x + 56$$ Simplify: $$100 = 74 + x$$ Subtract 74 from both sides: $$100 - 74 = x$$ $$x = 26$$ 7. **Summary for Venn diagram:** - Spinning only: 8 - Both classes: 10 - Circuits only: 26 - Neither: 56 This completes the data needed to draw the Venn diagram with two overlapping circles inside a rectangle representing the universal set of 100 people.