Question

A monospaced font is a font in which all characters are exactly of same width. A document uses a monospaced font for typesetting where each character is exactly 0.6 cm wide. A text line in this document contains only 10 words, where each word contains 6 characters. What is the length of the line in cm?
 

Answer 1

Correct Answer: 41.4

Step 1: The line holds ten words of six characters each. The characters alone take up \( 10 \times 6 = 60 \) character widths.

Step 2: A single space separates each pair of neighboring words. With ten words there are nine gaps between them, adding \( 9 \) more character widths.

Step 3: The line's total width in character units is \( 60 + 9 = 69 \). At \( 0.6 \) cm per character width, this comes to \( 69 \times 0.6 = 41.4 \) cm.
\[ \boxed{41.4 \text{ cm}} \]

Answer 2

This approach sets up a general formula for the length of any line of equal length words in this font. It then substitutes the numbers given in the question, instead of adding up the specific characters and spaces by hand.

Take a line of \( n \) words, each \( w \) characters wide, in a font where every character takes up \( c \) cm. The characters alone need \( nw \) character widths. The \( n - 1 \) gaps between the words add \( n - 1 \) more. So the total character width is \( nw + (n - 1) \). Multiplying by the width of one character gives the general formula \( L = c \left[ nw + (n - 1) \right] \).

Substituting \( c = 0.6, n = 10, \) and \( w = 6 \) gives \( L = 0.6 \left[ 10(6) + 9 \right] = 0.6 (60 + 9) = 0.6 (69) = 41.4 \) cm. the answer is \( 41.4 \) cm