Numeracy Foundation November 2018 Unit 1 Q9
9. A badge is made using a metal button, a pin and sticky tape.
Lulu’s Craft Shop
Pack of 42 metal buttons, only £2.50
Bag of 24 pins, only £1.10
60 cm roll of sticky tape, 52p
Elwyn decides to buy metal buttons and pins to make badges, so that there are no metal buttons or pins left over.
He wants to buy the least possible number of packs of metal buttons and bags of pins.
Show that Elwyn should buy 4 packs of metal buttons and 7 bags of pins.
You must show all your working. [2]
What is the maximum number of badges Elwyn can possibly make using 4 packs of metal buttons and 7 bags of pins? [1]
Each pin is stuck on to a metal button using approximately 2·5 cm of sticky tape.
Elwyn plans to sell the badges to make the maximum profit possible.
How many rolls of sticky tape should Elwyn buy? [3]
Number of rolls of sticky tape ....................
Elwyn sells all the badges he makes for 50p each.
Calculate the maximum profit he would make. [5]
| Scheme | Marks | Comments |
|---|---|---|
(i) Listing common multiples showing at least:
| B1 | Accept 6 × 7 (=42) AND 4 × 6 (=24), i.e. must have sight of factors which could lead to LCM being given, so do not accept e.g. 2 × 21 and 2 × 12 without further breakdown |
Complete listing:
( = 4 × 42 and 7 × 24) | B1 | Accept 6 × 4 × 7 or 6 × 2 × 2 × 7 If no marks, award SC1 for sight of 4 × 42 = 168 AND 7 × 24 = 168 (as least not shown), or indication that number of buttons and pins both 168 |
| (ii) 168 | B1 | CAO |
| Scheme | Marks | Comments | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| (i) (Sticky tape needed is) 2.5 × 4 × 42 or 2.5 × 7 × 24 or 2.5 × 168 (= 420 cm) | M1 | FT ‘their 168’ from (a)(ii) | |||||||||||||||
| (Number of rolls of sticky tape is) (2.5×4×42) ÷ 60 or (2.5×7×24) ÷ 60 or (2.5×168) ÷ 60 or 420 ÷ 60 | M1 | FT ‘their 168’ from (a)(ii) Allow sight of repeated addition of 60s, need to show 60, 120, 180, 240, 300 | |||||||||||||||
| 7 (rolls needed) | A1 | Only FT if number of rolls is >1 Must be rounded up to a whole number of rolls Allow 2.5cm rounded to 2cm or 3cm, FT as with use of 2.5cm
|
Alternative method (b)(i)
| Scheme | Marks | Comments | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 60 ÷ 2.5 (= 24 badges per roll of tape) | M1 | FT ‘their 168’ from (a)(ii) | |||||||||||||||
| (Number of rolls of sticky tape is) 168 ÷ (60 ÷ 2.5) or 168 ÷ 24 | M1 | FT ‘their 168’ from (a)(ii) | |||||||||||||||
| 7 (rolls needed) | A1 | Only FT if number of rolls is >1 Must be rounded up to a whole number of rolls Allow 2.5cm rounded to 2cm or 3cm, FT as with use of 2.5cm
|
| Scheme | Marks | Comments |
|---|---|---|
| (ii) Takings (50(p) × 168=) (£)84 or 8400(p) | B1 | FT ‘their 168’ from (a)(ii) |
| Costs 4×(£) 2.50 + 7×(£)1.10 | M1 | |
| + 7 × 52(p) | M1 | FT from (b)(i) ‘their number of rolls’ × 52p provided >1 |
| (=£10 + £7.70 + £3.64 =) (£) 21.34 | A1 | If units are given they must be correct FT £17.70 + 52p × ‘their number of rolls’, for any number of rolls |
| Profit (£84 – £21.34 =) (£) 62.66 | B1 | FT ‘their 84’ provided 50(p) × ‘their 168’ attempted and ‘their (£)21.34’ provided at least M1 previously awarded |