1. **State the problem:** We need to find the length of Beth's ribbon given the relationships between the lengths of Joan's, Sandra's, and Beth's ribbons and their total length. 2. **Define variables:** Let $B$ be the length of Beth's ribbon in cm. 3. **Express other ribbons in terms of $B$:** - Joan's ribbon is 34 cm shorter than Beth's: $J = B - 34$ - Sandra's ribbon is 20 cm longer than Beth's: $S = B + 20$ 4. **Write the equation for total length:** $$B + J + S = 268$$ Substitute $J$ and $S$: $$B + (B - 34) + (B + 20) = 268$$ 5. **Simplify the equation:** $$B + B - 34 + B + 20 = 268$$ $$3B - 14 = 268$$ 6. **Solve for $B$:** $$3B = 268 + 14$$ $$3B = 282$$ $$B = \frac{282}{3} = 94$$ 7. **Answer:** Beth's ribbon is 94 cm long. This solution uses basic algebra to set up an equation from the problem statement and solve for the unknown length.