1. **Problem statement:** A swimming club charges an annual fee and an hourly fee for pool time. Last year a member swam for 78 hours and paid 768, while another member swam for 102 hours and paid 912. Find the annual fee and hourly fee. 2. **Define variables:** Let $A$ be the annual fee and $h$ be the hourly fee. 3. **Set up the system of equations:** From the first member: $$A + 78h = 768$$ From the second member: $$A + 102h = 912$$ 4. **Subtract the first equation from the second to eliminate $A$:** $$\cancel{A} + 102h = 912$$ $$- (\cancel{A} + 78h = 768)$$ $$102h - 78h = 912 - 768$$ $$24h = 144$$ 5. **Solve for $h$:** $$h = \frac{144}{24} = 6$$ 6. **Substitute $h=6$ into the first equation to find $A$:** $$A + 78 \times 6 = 768$$ $$A + 468 = 768$$ $$A = 768 - 468 = 300$$ 7. **Answer:** The annual fee is 300 and the hourly fee is 6.