Higher June 2017 Paper 2 Q19
19 Rana sells 192 cakes in the ratio \(\quad\) small : medium : large \(\;=\; 7 : 6 : 11\)
- The profit for one medium cake is twice the profit for one small cake.
- The profit for one large cake is three times the profit for one small cake.
Her total profit is £532.48
Work out the profit for one small cake. [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(192 \div (7 + 6 + 11)\) or \(192 \div 24\) or 8 | M1 | May be implied |
| \(7 \times\) their 8 or 56 and \(6 \times\) their 8 or 48 and \(11 \times\) their 8 or 88 | M1dep | 56 : 48 : 88 is M2 |
| their 56 \((\times 1)\ +\) their 48 \(\times 2\) \(+\) their 88 \(\times 3\) or \(56 + 96 + 264\) or 416 | M1dep | May use \(x\), \(2x\) and \(3x\) (any letter) |
| \(532.48 \div\) their 416 | M1dep | Allow working in pence |
| 1.28 | A1 | |
| Alternative method 2 | ||
| \(7\ (\times 1) + 6 \times 2 + 11 \times 3\) or \(7 + 12 + 33\) or 52 | M1 | May use \(x\), \(2x\) and \(3x\) (any letter) |
| \(532.48 \div\) their 52 or 10.24 | M1dep | Allow working in pence |
| \(192 \div (7 + 6 + 11)\) or \(192 \div 24\) or 8 | M1 | May be implied |
| their \(10.24 \div\) their 8 | M1dep | dep on M3 oe eg their \(10.24 \times 7\) or 71.68 and their \(71.68 \div (7 \times\) their 8) |
| 1.28 | A1 | |
Additional guidance
| (Alt 1) 56 : 96 : 264 with no subsequent addition | M1M1M0M0A0 |
| \(532.48 \div 24\) (\(=\) 22.18… or 22.19) with no further valid working | Zero |
| \(532.48 \div 192\) (\(=\) 2.77…) with no further valid working | Zero |
| (Alt 1) 56 and 48 and 88 (or correct method leading to them) but not subsequently used | M2 |
| (Alt 1) 8 (or correct method leading to it) but not subsequently used | M1 |
| (Alt 2) 10.24 (or correct method leading to it) | M2 |
| 1.28 in working with Answer 71.68 (from \(1.28 \times 56\)) | M4A0 |