Higher November 2019 Paper 3 Q21
21 Juice is sold in small bottles and large bottles.
The volume of the large bottle is 1125 ml.
volume of small bottle : volume of large bottle = 2 : 5
A café has small glasses and large glasses.
volume of small glass : volume of large glass = 4 : 7
A small bottle fills 6 small glasses with no juice left over.
How many large glasses can be filled by a large bottle?
You must show your working. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(1125 \div 5 \times 2\) or 450 | M1 | oe |
| their \(450 \div 6 \times (7 \div 4)\) or \(75 \times 1.75\) or 131.25 | M1dep | |
| \(1125 \div\) their 131.25 | M1dep | |
| 8.57… or 8.6 or \(8\dfrac{4}{7}\) or 8 | A1 | |
| Alternative method 2 | ||
| \(5 \div 2\) or 2.5 and \(7 \div 4\) or 1.75 | M1 | oe |
| their \(2.5 \div\) their 1.75 or 1.42857… or \(\dfrac{10}{7}\) | M1dep | oe |
| \(6 \times\) their 1.42857… | M1dep | |
| 8.57… or 8.6 or \(8\dfrac{4}{7}\) or 8 | A1 | |
| Alternative method 3 | ||
| (Small bottle fills) \(6 \times \dfrac{4}{7}\) or \(\dfrac{24}{7}\) | M1 | |
| (Large bottle fills) their \(\dfrac{24}{7} \times \dfrac{5}{2}\) or \(\dfrac{120}{14}\) | M1dep | |
| their \(120 \div\) their 14 | M1dep | |
| 8.57… or 8.6 or \(8\dfrac{4}{7}\) or 8 | A1 | |
| Alternative method 4 | ||
| Any two of \(b_1 = 6g_1\) and \(b_2 = 2.5b_1\) and \(g_2 = 1.75g_1\) | M1 | oe any letters for small bottle (\(b_1\)), small glass (\(g_1\)), large bottle (\(b_2\)) and large glass (\(g_2\)) |
| \(b_2 = 2.5 \times 6g_1\) or \(b_2 = 15g_1\) | M1dep | oe |
| \(b_2 =\) their \(15\left(\dfrac{g_2}{1.75}\right)\) | M1dep | |
| 8.57… or 8.6 or \(8\dfrac{4}{7}\) or 8 | A1 | |
Additional guidance
| If the student attempts more than one method, mark each method and award the highest mark | |
| Correct answer seen in working, 9 on answer line | M1M1M1A0 |