A pencil has three colour segments in order. The first 1/8 of the whole pencil is black; half of the remaining length is white; the rest is blue. If the blue segment measures 3.5 cm, what is the total length of the pencil?

Introduction / Context:The question involves successive fractions applied to a whole. After removing the first fraction, another fraction of the remainder is taken, and the leftover is given in centimetres. We must backtrack to the total length. This is a typical fraction-of-a-remainder problem.

Given Data / Assumptions:

• Total length = L cm.
• Black segment = (1/8)L.
• Remaining after black = (7/8)L.
• White segment = (1/2) * (7/8)L = (7/16)L.
• Blue segment = remaining = (7/8)L - (7/16)L = (7/16)L.
• Blue segment length is 3.5 cm.

Concept / Approach:Set up the expression for the blue segment in terms of L and equate it to the given 3.5 cm to solve for L. Keep all calculations in centimetres for consistency.

Step-by-Step Solution:

Verification / Alternative check:Compute segments: black = 1/8 of 8 = 1; remaining = 7; white = half of 7 = 3.5; blue = 7 - 3.5 = 3.5. Totals add to 8 cm, matching L.

Why Other Options Are Wrong:

• 6, 7, 9, 10 cm: Substituting these values fails to keep the final blue length equal to 3.5 cm given the fractional splits.

Common Pitfalls:

• Taking half of the original instead of half of the remainder.
• Arithmetic errors when subtracting fractional parts.

Final Answer:8 cm