Numeracy Higher June 2022 Unit 1 Q2
2.
(a) Gwyn is making some packs.
Each pack contains one nut, one bolt and one washer.
Each pack contains one nut, one bolt and one washer.
To make up these packs, Gwyn buys:
- some boxes that contain 30 nuts each
- some boxes that contain 5 bolts each
- some boxes that contain 25 washers each.
Gwyn wants to buy the least possible number of boxes so that, in making up the packs, he uses all of the nuts, bolts and washers he has bought.
Complete the table below to show the number of boxes of each item that Gwyn needs to buy.
You must show all your working. [3]
| Number of boxes needed | |
|---|---|
| Nuts (30 in each box) | …………………… boxes |
| Bolts (5 in each box) | …………………… boxes |
| Washers (25 in each box) | …………………… boxes |
(b) Each washer has a thickness of 2 mm, correct to the nearest 0·5 mm.
Calculate the greatest possible thickness of a stack of 6 washers. [2]
Calculate the greatest possible thickness of a stack of 6 washers. [2]
| Scheme | Marks | Comments | ||||||
|---|---|---|---|---|---|---|---|---|
| Lowest common multiple of 2 × 3 × 5 × 5 or 150 seen or implied, e.g. listing multiples to 150 for nuts and washers and sight of 30 boxes of bolts, sight of 5 × 30 = 150, 6 × 25 = 150 and sight of 30 boxes of bolts, | M2 | M1 for a method looking at factors or multiples, e.g.
| ||||||
Table completed correctly, or sight of correct number of boxes in working, e.g.
| A1 | Answers in the table take precedence, e.g. if correct number of boxes 5 for nuts, 30 for bolts and 6 for washers in working but table incorrect, award M2 A0 If no marks, award SC1 for an answer with whole numbers of nuts, bolts and washers in the ratio 5:30:6, e.g. answers of 10, 60 and 12 respectively |
| Scheme | Marks | Comments |
|---|---|---|
| 13.5(0 mm) | B2 | B1 for sight of any one of:
|