Intermediate June 2019 Unit 1 Q17
17. Arthur, Sian and Kezia are all given some £1 coins.
Arthur receives £\(n\).
Sian is given five times as much money as Arthur.
Kezia receives three times as much money as Arthur, plus an extra £7.
Sian was given less money than Kezia.
(a) Write down an inequality in terms of \(n\) that illustrates the fact that Sian received less money than Kezia. [2]
(b) What was the greatest amount of money that Arthur could have been given? [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(5n \lt 3n + 7\) or equivalent ISW | B2 | \(2n \lt 7\) OR \(n \lt 7/2\) implies B2. Ignore use of a different letter e.g. \(5x \lt 3x + 7\). Use of ‘≤’ is B1. B1 for sight of \(3n + 7\) in an inequality. |
| Scheme | Marks | Comments |
|---|---|---|
| \(2n \lt 7\) OR \(n \lt 7/2\) | B1 | FT ‘their inequality’ if of equivalent difficulty. May be seen in part (a). |
| (Greatest amount =) (£)3 | B1 | FT ‘their \(n \lt k\)’. B0 if they have ‘\(n\gt k\)’. B0 if it leads to \(n\lt 1\) An answer of (£)3 gains B1B1 (unless from incorrect algebra work). |