Foundation November 2017 Paper 3 Q9
9 A farmer has 580 eggs to put into boxes.
The boxes come in three sizes.
He wants
at least 10 boxes of 20 eggs
at least 15 boxes of 12 eggs
at least 25 boxes of 6 eggs.
The farmer fills 54 boxes with the 580 eggs.
Show how he does this. [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(10 \times 20\) or 200 and \(15 \times 12\) or 180 and \(25 \times 6\) or 150 | M1 | |
| \(10 \times 20 + 15 \times 12 + 25 \times 6\) or their 200 + their 180 + their 150 or 530 | M1dep | |
| 580 – their 530 or 50 (eggs) | M1dep | |
| 54 – (10 + 15 + 25) or 54 – 50 (boxes) or 4 (more boxes) or 1 (+) 2 (+) 1 | M1 | |
| 11 boxes of 20 17 boxes of 12 26 boxes of 6 | A1 | |
| Alternative method 2 | ||
| 11 boxes of 20 17 boxes of 12 26 boxes of 6 | B5 | B4 for 11 boxes of 20 16 boxes of 12 28 boxes of 6 or 11 boxes of 20 15 boxes of 12 30 boxes of 6 B3 for 580 eggs placed in boxes with two of these conditions satisfied at least 10 boxes of 20 eggs at least 15 boxes of 12 eggs at least 25 boxes of 6 eggs B2 for 580 eggs placed in boxes with one of the three conditions satisfied and at least one of each box B1 for all three conditions satisfied with 54 boxes but a total number of eggs not equal to 580 |
Additional guidance
| Fourth M1 mark may be awarded at any stage | |
| 10 + 15 + 25 = 50 is a total of boxes and does not score M1M1M1 | |
| 1 (extra) boxes of 20 2 (extra) boxes of 12 1 (extra) boxes of 6 | M1M1M1M1A1 |
| 220, 204 and 156 (eggs) on answer line with 11, 17 and 26 (boxes) seen in working | B5 |
| Condone number of eggs on answer line if number of boxes seen in working eg 220, 240 and 120 (eggs) on answer line with 11, 20 and 20 (boxes) seen in working | B3 |