Final answer:
The students must have baked at least 19 pies, given that each pie is cut into 8 pieces and at least 224 pieces were sold, including the 9 pies donated by the cafeteria.
Step-by-step explanation:
To determine how many pies the students baked, we need to calculate the number of pies based on the pie pieces sold. We know that each pie is cut into 8 pieces, and at least 224 pieces were sold. Along with the 9 pies donated by the cafeteria, we would write an equation: number of student-baked pies * 8 (pieces per pie) + 9 (cafeteria pies) * 8 (pieces per pie) ≥ 224 (pieces sold). We simplify to find the number of student-baked pies.
The equation to calculate the pies baked by the students becomes: student pies * 8 + 72 ≥ 224. We subtract 72 from both sides to isolate the student pies variable, which gives us student pies * 8 ≥ 152. Finally, we divide both sides by 8 to find the number of student-baked pies: student pies ≥ 19. Therefore, the minimum number of pies the students must have baked is 19.