1. **State the problem:** We need to find the values of $A$, $B$, and $C$ so that the sum of the numbers on each line equals 9. 2. **Identify the lines and their sums:** - Top vertical line: $4 + A + 3\frac{1}{2} + 1\frac{1}{2} = 9$ - Middle horizontal line: $A + 3\frac{1}{2} + B + C = 9$ - Bottom vertical line: $3\frac{1}{2} + B + 1 = 9$ 3. **Convert mixed numbers to improper fractions or decimals for easier calculation:** - $3\frac{1}{2} = 3.5$ - $1\frac{1}{2} = 1.5$ 4. **Solve the top vertical line for $A$:** $$4 + A + 3.5 + 1.5 = 9$$ $$4 + A + 5 = 9$$ $$A + 9 = 9$$ $$A = 9 - 9 = 0$$ 5. **Solve the bottom vertical line for $B$:** $$3.5 + B + 1 = 9$$ $$B + 4.5 = 9$$ $$B = 9 - 4.5 = 4.5$$ 6. **Use the middle horizontal line to solve for $C$:** $$A + 3.5 + B + C = 9$$ Substitute $A=0$ and $B=4.5$: $$0 + 3.5 + 4.5 + C = 9$$ $$8 + C = 9$$ $$C = 9 - 8 = 1$$ 7. **Final answers:** - $A = 0$ - $B = 4.5$ - $C = 1$