Foundation November 2024 Paper 1 Q14
14 Five adults and two children go to a theme park.
The cost of an adult ticket is £6 more than the cost of a child ticket.
The total cost of the seven tickets is £142.
Work out the cost of an adult ticket.
You must show your working. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 22 with correct working | 5 | Correct answer from trials scores 5 “Correct working” requires evidence of at least 3 method marks | |
| Finding adult cost (a) directly: M3 for \(5a + 2a - 12 = 142\) or M2 for \(5a + 2(a - 6)\) or M1 for \(a - 6\) M1 for \(7a = 154\) OR M2 for 142 + 12 or M1 for \(6 \times 2\) used, may be implied by use of 12 M1 for their\((142 + 12) \div 7\) | Finding child cost (c) first: M3 for \(5c + 2c + 30 = 142\) or M2 for \(5(c + 6) + 2c\) or M1 for \(c + 6\) M1 for \(7c = 112\) or \(c = 16\) OR M2 for 142 – 30 or M1 for \(6 \times 5\) used, may be implied by use 30 M1 for their \((142 - 30) \div 7\) M1 for their\((142 - 30) \div 7 + 6\) | ||
| Simultaneous Equations M1 for \(5a + 2c = 142\) M1 for \(a - c = 6\) M1 for correct method to equate coefficients of one variable, allow one arithmetic error M1 for correct method to eliminate one variable, allow one arithmetic error | Trials: M3 for correctly evaluated trial using [\(a =\)] 22 and [\(c =\)] 16 or M2 for two correctly evaluated trials where \(c = a - 6\) or M1 for one correctly evaluated trial where \(c = a - 6\) | ||
| If 0 or 1 scored, instead award SC2 for 22 with no working or insufficient working If 0 scored instead award SC1 for 16 with no working or insufficient working | |||