1. **Problem Statement:** In a country club of 144 people, 61 play football, 65 play baseball, and 72 play hockey. 22 play all three games, 11 play none, and an equal number play only two games. We need to find: (i) How many play only two games? (ii) How many play only football? 2. **Given Data:** - Total people, $N = 144$ - Football players, $F = 61$ - Baseball players, $B = 65$ - Hockey players, $H = 72$ - Play all three, $F \cap B \cap H = 22$ - Play none, $N_0 = 11$ - Equal number play only two games, let this number be $x$ 3. **Define variables for only two games:** - Only Football and Baseball: $x$ - Only Baseball and Hockey: $x$ - Only Football and Hockey: $x$ 4. **Define variables for only one game:** - Only Football: $f$ - Only Baseball: $b$ - Only Hockey: $h$ 5. **Use the total count equation:** $$f + b + h + 3x + 22 + 11 = 144$$ Here, $3x$ because there are three pairs of two-game players each with $x$ people. Simplify: $$f + b + h + 3x = 144 - 22 - 11 = 111$$ 6. **Use the individual sport totals:** For Football: $$f + x + x + 22 = 61 \Rightarrow f + 2x = 39$$ For Baseball: $$b + x + x + 22 = 65 \Rightarrow b + 2x = 43$$ For Hockey: $$h + x + x + 22 = 72 \Rightarrow h + 2x = 50$$ 7. **Sum the three equations:** $$(f + b + h) + 6x = 39 + 43 + 50 = 132$$ 8. **Recall from step 5:** $$f + b + h + 3x = 111$$ Subtract step 5 from step 7: $$(f + b + h) + 6x - (f + b + h + 3x) = 132 - 111$$ $$3x = 21 \Rightarrow x = 7$$ 9. **Find $f$, $b$, and $h$:** From step 6: $$f + 2(7) = 39 \Rightarrow f = 39 - 14 = 25$$ $$b + 14 = 43 \Rightarrow b = 29$$ $$h + 14 = 50 \Rightarrow h = 36$$ 10. **Final answers:** (i) Number who play only two games = $x = 7$ (ii) Number who play only football = $f = 25$