Higher June 2025 Paper 6 Q7
7 Each member of a tennis club is classed as a junior, an adult or a senior.
- 16% of the members are seniors.
- The ratio of the number of juniors to the number of adults is 9 : 5.
- There are 95 more juniors than seniors.
Work out the total number of members of the tennis club.
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 250 with correct working | 6 | M2 for \(\frac{100 - 16}{9 + 5} \times 9\) oe or \(\frac{100 - 16}{9 + 5} \times 5\) oe or M1 for \(\frac{100 - 16}{9 + 5}\) oe may be implied by 6 | Correct working requires evidence of at least M1 or B1 AND M1 Where there is a choice of method, mark the one that is progressed furthest |
| AND B1 for 54 and 30 AND | |||
| M2 for (54 and 30 and 16) × \(\frac{95}{54 - 16}\) oe or for \(\frac{95}{54 - 16}\) × 100 oe or M1 for \(\frac{95}{54 - 16}\) oe may be implied by 2.5, 135, 75 or 40 | May be seen with + signs, as a ratio, or as three separate products Alternative second stage by trials (in addition to any marks received for the first stage) M2 for 135 : 75 : 40 or M1 for 108 : 60 : 32 and 162 : 90 : 48 | ||
| If 0 or 1 scored, instead award SC2 for 250 with no or insufficient working If 0 scored, instead award SC1 for 54 or 30 with no or insufficient working | Algebra in terms of juniors j M1 for \(a = \frac{5}{9}j\) oe M1 for \(s = j - 95\) oe AND M1 for \(j - 95 = \frac{16}{100}\left(j - 95 + j + \frac{5}{9}j\right)\) oe or better A1 for \(j = 135\) M1 for \(s = 135 - 95\) implied by 40 and \(a = \frac{5}{9} \times 135\) implied by 75 | ||
| Starting from ratio j : a is 9x : 5x M2 for \(9x - 95 = 0.16(9x + 5x + 9x - 95)\) oe or better A1 for \(x = 15\) or M1 for \(s = 9x - 95\) or \(s = 0.16(9x + 5x + 9x - 95)\) oe or better AND M2 for 23 × 15 – 95 oe or M1 for \(a = 5 \times 15\) implied by 75 or \(j = 9 \times 15\) implied by 135 or \(s = 9 \times 15 - 95\) implied by 40 If 0 or 1 scored, instead award SC2 for 250 with no or insufficient working If 0 scored, instead award SC1 for 15 with no or insufficient working | Algebra in terms of adults a M1 for \(j = \frac{9}{5}a\) oe M1 for \(s = \frac{9}{5}a - 95\) oe AND M1 for \(\frac{9}{5}a - 95 = \frac{16}{100}\left(a + \frac{9}{5}a + \frac{9}{5}a - 95\right)\) oe or better A1 for \(a = 75\) M1 for \(j = \frac{9}{5} \times 75\) implied by 135 and \(s = \frac{9}{5} \times 75 - 95\) implied by 40 | ||
| Algebra in terms of total t M1 for \(s = 0.16t\) M1 for \(j = 0.16t + 95\) M1 for \(a = \frac{5}{9}(0.16t + 95)\) AND M2 for \(t = 0.16t + 0.16t + 95 + \frac{5}{9}(0.16t + 95)\) oe or better | Algebra in terms of seniors s M1 for \(j = s + 95\) oe M1 for \(a = \frac{5}{9}(s + 95)\) oe AND M1 for \(s = \frac{16}{100}\left(s + s + 95 + \frac{5}{9}(s + 95)\right)\) oe or better A1 for \(s = 40\) M1 for \(j = 40 + 95\) implied by 135 and \(a = \frac{5}{9}(40 + 95)\) implied by 75 | ||