1. **State the problem:** We are given gallons per minute (gpm) for sections B, C, D, E, F, and G, and several inequalities involving section A's gpm. We need to determine the possible range or value of gallons per minute for section A. 2. **Given data:** - B: $6$ m - C: $14$ m - D: $8$ m - E: $12$ m - F: $7$ m - G: $10$ m 3. **Inequalities involving A:** - A receives fewer gallons than D and more than B: $6 < A < 8$ - A receives fewer gallons than E and more than F: $7 < A < 12$ - A receives more gallons than C and fewer than D: $14 < A < 8$ (contradiction here, so check carefully) - A receives more gallons than F and fewer than G: $7 < A < 10$ 4. **Analyze the inequalities:** - From first: $6 < A < 8$ - From second: $7 < A < 12$ - From third: $A > 14$ and $A < 8$ is impossible, so likely a typo or misread; since it contradicts, ignore or clarify. - From fourth: $7 < A < 10$ 5. **Combine consistent inequalities:** - $6 < A < 8$ - $7 < A < 12$ - $7 < A < 10$ 6. **Find intersection:** - The intersection of $6 < A < 8$ and $7 < A < 12$ is $7 < A < 8$ - The intersection of $7 < A < 8$ and $7 < A < 10$ is still $7 < A < 8$ 7. **Final conclusion:** - Section A receives between 7 and 8 gallons per minute. **Answer:** $$7 < A < 8$$