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?
 

Hint:

In monospaced font problems, always multiply the number of characters by the width of each character, then add extra space for separation between words.

Answer 1

The problem requires calculating the total length of a text line in a document that uses a monospaced font where each character is exactly \(0.6 \, \text{cm}\) wide. The line contains 10 words, each consisting of 6 characters. 

Step 1: Understanding the problem Each word consists of \(6\) characters. There are \(10\) words in the line. Each character occupies a width of \(0.6 \, \text{cm}\). A space is present between each pair of words. Since there are \(10\) words, there will be \(9\) spaces in total. Each space also occupies \(0.6 \, \text{cm}\), as the font is monospaced.

Step 2: Calculating the total length of the line The total width contributed by the characters in the 10 words: \[ \text{Width of characters} = 10 \, (\text{words}) \times 6 \, (\text{characters per word}) \times 0.6 \, \text{cm} = 36 \, \text{cm}. \] The total width contributed by the spaces between the words: \[ \text{Width of spaces} = 9 \, (\text{spaces}) \times 0.6 \, \text{cm} = 5.4 \, \text{cm}. \] The total length of the line is the sum of the two contributions: \[ \text{Total length} = 36 \, \text{cm} + 5.4 \, \text{cm} = 41.4 \, \text{cm}. \] 

Conclusion The length of the text line in the document is: \[ \boxed{41.4 \, \text{cm}}. \]

Answer 2

This question asks for the length of a text line set in a monospaced font, where every character, including the space between words, takes up exactly 0.6 cm. There is only one line to measure, so instead of solving it in separate pieces, we can treat the whole line as one string of equal-width slots and count how many slots it has.

Each of the 10 words has 6 characters, so the letters alone use up \[ 10 \times 6 = 60 \] character slots.
Between 10 words there are always 9 gaps, one gap after each word except the last, and in a monospaced font each of these gaps is also exactly one character slot wide.
Adding the letter slots and the gap slots together gives the total number of slots in the line: \[ 60 + 9 = 69 \] slots.
Since every slot, whether it holds a letter or a space, is 0.6 cm wide, the total length of the line is \[ 69 \times 0.6 = 41.4\, \text{cm}. \]

So the length of the text line is 41.4 cm.