Higher June 2023 Paper 1 Q11
11. The table shows some information about the cost per person to take a boat across a river.
| Adults (£) | a |
| Children (£) | c |
The Jones family of 4 adults and 1 child pay £9.50 to take the boat.
The Patel family of 5 adults and 2 children pay £13 to take the boat.
The Lee family has 3 adults and 2 children.
How much does the Lee family pay to take the boat?
You must use an algebraic method and show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| \(4a + c = 9.5(0)\) AND \(5a + 2c = 13\) oe | B1 | Allow other letters or words throughout. Values may be in pence throughout |
| Method to eliminate an unknown e.g. equal coefficients and subtraction or rearranges one equation and substitutes into the other | M1 | FT their equations provided one is correct and the other is linear in the same pair of unknowns. Allow one error in one term, not in the equated coefficients. Allow one error in rearrangement but not substitution. |
| Finds one unknown | A1 | CAO; \(a = 2\) or \(c = 1.5(0)\) |
| Finds the other unknown | A1 | FT ‘their \(a\)’ or ‘their \(c\)’ used in one of their equations. |
| (£)9(.00) or 900(p) | B1 | Provided at least two of the previous four marks awarded, FT 3(‘their derived \(a\)’) + 2(‘their derived \(c\)’) If units are given, they must be correct. For candidates that are awarded B1 and use trials to find the values of a and c, award SC2 for a final answer of (£)9(.00) or 900(p). |
| (5) |