Higher June 2022 Paper 3 Q3
3 Rick, Selma and Tony are playing a game with counters.
Rick has some counters.
Selma has twice as many counters as Rick.
Tony has 6 counters less than Selma.
In total they have 54 counters.
the number of counters Rick has : the number of counters Tony has \(= 1 : p\)
Work out the value of \(p\). (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 1.5 | P1 | for process to develop 3 algebraic expressions, eg (\(R =\)) \(n\), (\(S =\)) \(2n\), (\(T =\)) \(2n - 6\), oe, at least two must be correct. or for selecting 3 values satisfying the given criteria, eg (\(R =\)) 10, (\(S =\)) 20, (\(T =\)) 14 |
| P1 | for process to sum 3 algebraic expressions and equating to 54, eg \(n + \text{``}2n\text{''} + \text{``}2n - 6\text{''} = 54\) or for finding the correct sum of their values eg \(\text{``}10\text{''} + \text{``}20\text{''} + \text{``}14\text{''} = 44\) | |
| P1 | for start of process to solve the correct linear equation, eg \(5n = 54 + 6\ (n = 12)\) or for 12, 24, 18 | |
| P1 | for \(\text{``}12\text{''} : 2 \times \text{``}12\text{''} - 6\) oe eg \(12 : 18\) oe or \(18 : 12\) linked to T, R | |
| A1 | for 1.5 or \(\dfrac{3}{2}\) or \(1\frac{1}{2}\) |
Additional guidance
Accept \(1 : 1.5\) etc as answer