1. **State the problem:** We have a bag with three types of counters: green triangles, green circles, and yellow circles. We know: - 70% of the green counters are circles. - 40% of the circular counters are green. - There are 21 yellow counters. We need to find the number of green triangular counters. 2. **Define variables:** Let $G$ be the total number of green counters. Let $C$ be the total number of circular counters. Let $T$ be the number of green triangular counters. 3. **Translate the percentages into equations:** - Since 70% of green counters are circles, green circles = $0.7G$. - Therefore, green triangles = $G - 0.7G = 0.3G$. - Since 40% of circular counters are green, green circles = $0.4C$. 4. **Relate green circles from both perspectives:** Green circles = $0.7G = 0.4C$. 5. **Express $C$ in terms of $G$:** $$0.7G = 0.4C \implies C = \frac{0.7G}{0.4} = 1.75G$$ 6. **Total counters:** The counters are green triangles, green circles, and yellow circles. Total counters = green triangles + green circles + yellow counters $$= 0.3G + 0.7G + 21 = G + 21$$ 7. **Total circular counters $C$ include green circles and yellow circles:** $$C = \text{green circles} + \text{yellow circles} = 0.7G + 21$$ 8. **Recall from step 5 that $C = 1.75G$, so:** $$1.75G = 0.7G + 21$$ 9. **Solve for $G$:** $$1.75G - 0.7G = 21$$ $$1.05G = 21$$ $$G = \frac{21}{1.05} = 20$$ 10. **Find the number of green triangles $T$:** $$T = 0.3G = 0.3 \times 20 = 6$$ **Final answer:** There are **6** green triangular counters.