1. **Problem statement:** A drinking straw of length 21 cm is cut into 3 pieces. - The first piece has length $x$ cm. - The second piece is 3 cm shorter than the first piece, so its length is $x - 3$ cm. - The third piece's length is unknown, but the total length of all three pieces is 21 cm. 2. **Express lengths of each piece:** - First piece: $x$ - Second piece: $x - 3$ - Third piece: Since total length is 21 cm, third piece length is $21 - (x + (x - 3))$ 3. **Simplify the third piece length:** $$21 - (x + x - 3) = 21 - (2x - 3) = 21 - 2x + 3 = 24 - 2x$$ 4. **Sum of lengths expression:** Sum of all pieces = first + second + third $$x + (x - 3) + (24 - 2x)$$ Simplify: $$x + x - 3 + 24 - 2x = (x + x - 2x) + (24 - 3) = 0 + 21 = 21$$ 5. **Calculate $x$:** Since the sum equals 21, the expression is consistent for any $x$ that makes the third piece length non-negative. 6. **Find $x$ such that all pieces have positive length:** - Second piece length $x - 3 > 0 \Rightarrow x > 3$ - Third piece length $24 - 2x > 0 \Rightarrow 24 > 2x \Rightarrow x < 12$ Therefore, $x$ must satisfy $3 < x < 12$. 7. **Final answer:** - Lengths: first piece $x$ cm, second piece $x - 3$ cm, third piece $24 - 2x$ cm. - Sum expression: $x + (x - 3) + (24 - 2x) = 21$ - $x$ can be any value between 3 and 12 to keep all pieces positive. Since the problem asks to calculate $x$, assuming all pieces are positive, $x$ can be any value in $(3,12)$. If the problem expects a specific value, more information is needed. **Summary:** - (a) Pieces: $x$, $x - 3$, $24 - 2x$ - (b) Sum: $x + (x - 3) + (24 - 2x) = 21$ - (c) $x$ satisfies $3 < x < 12$ to keep all pieces positive.