Foundation November 2018 Paper 3 Q23
23 At a café,
2 teas and 1 coffee cost £3.40
1 tea and 4 coffees cost £7.30
Work out the cost of 1 tea and the cost of 1 coffee. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 – Elimination | ||
| \(2t + c = 3.4(0)\) and \(2t + 8c = 14.6(0)\) | M1 | oe \(8t + 4c = 13.6(0)\) and \(t + 4c = 7.3(0)\) allow one error in scaling equations |
| \(8c - c = 14.6(0) - 3.4(0)\) or \(7c = 11.2(0)\) | M1dep | oe \(8t - t = 13.6(0) - 7.3(0)\) or \(7t = 6.3(0)\) |
| \(c = 1.6(0)\) or 160 | A1 | \(t = 0.9(0)\) or 90 |
| (Tea) £0.90 or 90p and (Coffee) £1.60 or 160p | A1 | must be correct units |
| Alternative method 2 – Substitution | ||
| \(t = \dfrac{3.4(0) - c}{2}\) or \(t = 7.3(0) - 4c\) | M1 | oe \(c = 3.4(0) - 2t\) or \(c = \dfrac{7.3(0) - t}{4}\) |
| \(\dfrac{3.4(0) - c}{2} + 4c = 7.3(0)\) or \(2(7.3(0) - 4c) + c = 3.4(0)\) | M1dep | oe \(t + 4(3.4(0) - 2t) = 7.3(0)\) or \(2t + \dfrac{7.3(0) - t}{4} = 3.4(0)\) |
| \(c = 1.6(0)\) or 160 | A1 | \(t = 0.9(0)\) or 90 |
| (Tea) £0.90 or 90p and (Coffee) £1.60 or 160p | A1 | must be correct units |
| Alternative method 3 | ||
| A correctly evaluated trial of a value for tea and a value for coffee satisfying one statement and then substituted into the other statement | M1 | eg £1 + £1 + £1.40 = 3.4(0) and £1 + 4 \(\times\) £1.40 = 6.6(0) |
| A different correctly evaluated trial | M1dep | |
| (Tea) 0.9(0) or 90 and (Coffee) 1.6(0) or 160 or a correctly evaluated trial with (Tea) 0.9(0) or 90 and (Coffee) 1.6(0) or 160 | A1 | |
| (Tea) £0.90 or 90p and (Coffee) £1.60 or 160p | A1 | must be correct units |
Additional guidance
| Ignore incorrect trials alongside correct trials | |
| Condone £1.60p or £0.90p | |
| Allow working in pence | |
| In Alt1 the 2nd method mark can be scored following one error in scaling equations in the 1st method mark | |
| Both prices correct with no or insufficient working | M1M1A1A1 |
| Tea 160p and Coffee 90p on answer line with no or insufficient working | M1M1A1A0 |
| One price correct (with other price incorrect) and no or insufficient working eg Tea 90p and Coffee 140p with no or insufficient working | M0M0A0A0 |