Higher June 2023 Paper 6 Q9
9 On Heidi’s bookcase, the ratio of fiction to non-fiction books is 2 : 3.
Heidi removes 2 fiction books from the bookcase.
The ratio of fiction to non-fiction books is then 5 : 8.
How many books are left on the bookcase in total? [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 78 | 4 | Ratios: B3 for 32 : 48 and 30 : 48 identified or for 32 : 48 : 30 or M2 for \(16k : 24k\) and \(15k : 24k\) or for \(16k : 24k : 15k\) where \(k\) is a positive integer or for \(\frac{2}{3} - \frac{5}{8}\) oe implied by \(\frac{1}{24}\) or M1 for \(16k : 24k\) or \(15k : 24k\) where \(k\) is a positive integer or for \(\frac{2}{3}\) or \(\frac{5}{8}\) or \(\frac{2}{5}\) or \(\frac{3}{5}\) or \(\frac{5}{13}\) or \(\frac{8}{13}\) or their reciprocals seen or used Listing: M3 for multiples of 13 reaching at least 78 and multiples of 5 reaching at least 80 or for reaching 39 and 40 and then doubling or M2 for listing multiples of 13 and 5 reaching at least 39 and 40 or M1 for listing at least three multiples of 13 and 5 Fractions and ratios: B3 for \(\frac{32}{80} : \frac{48}{80}\) and \(\frac{30}{78} : \frac{48}{78}\) identified or M2 for \(\frac{16}{40} : \frac{24}{40}\) and \(\frac{15}{39} : \frac{24}{39}\) or M1 for \(\frac{16}{40} : \frac{24}{40}\) or \(\frac{15}{39} : \frac{24}{39}\) All methods: If 0 scored SC1 for answer 30, 32, 48 or 80 | Alternative methods using equations: M2 for correct unsimplified equation(s) to find original or new numbers of fiction, non-fiction or total A1 for correct solution(s) of the equation(s), no FT or M1 for one correct equation involving two variables eg using t as new total M2: \(\frac{3}{5}(t + 2) = \frac{8}{13}t\) oe \(\frac{2}{5}(t + 2) - \frac{5}{13}t = 2\) oe should lead to [\(t\) = ] 78, full marks eg using t as old total M2: \(\frac{3}{5}t = \frac{8}{13}(t - 2)\) oe \(\frac{2}{5}t - \frac{5}{13}(t - 2) = 2\) oe A1: [\(t\) = ] 80 eg using f as new number of fiction, \(n\) as number of non-fiction M2: \(8f = 5n\) and \(3(f + 2) = 2n\) A1: \(f = 30\) and \(n = 48\) eg using f as old number of fiction, \(n\) as number of non-fiction M2: \(8(f - 2) = 5n\) and \(3f = 2n\) A1: \(f = 32\) and \(n = 48\) eg M1: \(8f = 5n\) or \(3(f + 2) = 2n\) or \(8(f - 2) = 5n\) or \(3f = 2n\) |