Foundation June 2023 Paper 3 Q21

21 The length of a word is classed as short, medium or long depending on the number of characters in the word.

This table shows the percentage, in terms of \(x\), of each word length found in a book.

Find the percentage of words in this book which are classed as short words.
You must show your working. [5]

Mark scheme

Answer	Marks	Part marks and guidance
37 with correct working	5	M1 for \(2x + 5 + 3x - 1 + x = 100\) may be implied by a subsequent correct equation M1 for simplifying their equation to \(ax + b = c\) or \(6x + 4 = 100\) M1 for the first correct step in solving their \(ax + b = c\) and M1 for substituting their 16 into \(2x + 5\) OR M3 for one complete correct evaluation of \(2x + 5 + 3x - 1 + x = 100\) or M2 for one complete correct evaluation of \(2x + 5 + 3x - 1 + x =\) a total or M1 for one correct evaluation of each expression \(2x + 5\) [+] \(3x - 1\) [+] \(x\) If 0, 1 or 2 scored, instead award SC3 for answer 37 with no or insufficient working If 0 or 1 scored, instead award SC2 for \(x = 16\) with no or insufficient working	“Correct working” requires evidence of first method and at least M1 and \(x = 16\) or M3 if using trials or M2M1 for non-algebraic method Three separate expressions are not enough Ignore inclusion of % in working \(6x + 4 = 100\) scores M1M1 e.g. \(6x = 100 - 4\) \(6x = 96\) scores M1M1M1 For M marks with trials: allow each term or each expression from the question evaluated separately e.g. (Use 10) 20 + 5 + 30 – 1 + 10 = 64 or 25 (+) 29 (+) 10 = 64 Alternative method (Non algebraic) M2 for 100 – 5 + 1 oe or M1 for – 5 + 1 or – 4 AND M1 for their \((100 - 5 + 1) \div 6\) AND M1 for substituting their 16 into \(2x + 5\)