Numeracy Intermediate June 2023 Unit 2 Q3
3.
In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
The Draig Afon youth choir went on tour.
48 people travelled and stayed in hotels.
The organiser booked:
- Gwesty Arwel for 3 nights
- Hotel Glan y Môr for 5 nights.
The table gives the prices per night for the two hotels.
Gwesty Arwel
Group bookings get a discount of 14% | Hotel Glan y Môr
|
The Draig Afon youth choir qualified for the group booking offer.
12 of these people required single rooms.
The other 36 people were booked into twin rooms.
Calculate the total cost of the 8-night stay for the choir.
You must show all your working. [8 + 2 OCW]
The Draig Afon youth choir hired a coach.
At the start of the tour, the coach’s display showed it had travelled 32 474 km.
At the end of the tour, the coach’s display showed 33 860 km.
The fuel for the coach cost £1.86 per litre.
On average, the coach used 1 litre of fuel for every 4 km travelled.
Calculate the total cost of the fuel used for the choir’s tour. [5]
| Scheme | Marks | Comments |
|---|---|---|
| Gwesty Arwel (costs are) (1 night: 12 single rooms and 18 twin rooms) (84 × 12 and 102 × 36 ÷ 2) (£)1008 and (£)1836 OR (£)2844 OR (3 nights 12 single rooms and 18 twin rooms) (3 × 84 × 12 and 3 × 102 × 36 ÷ 2) (£)3024 and (£)5508 OR (£)8532 | B2 | B2 or B1 may be seen or implied in further working B1 for any one of the following:
|
| (Total discounted cost for 3 nights) 84 × 12 + 102 × 36 ÷ 2 × 3 × (1 – 0.14) | M1 M1 | For both M marks, awarded in either order, FT ‘their cost of single rooms + twin rooms’ Calculations may be shown separately as single rooms and twin rooms, but must include intention to add costs in further working |
| (£) 7337.52 | A1 | CAO If M1 M0 A0, award SC1 for (£)1194.48 or correctly evaluated total discount for ‘their 3 nights’ |
| Hotel Glan y Môr (costs for 5 nights are) 12 × 58 + 36 × 34 (× 5) or (696 + 1224) (× 5) or 1920 (× 5) or 3480 + 6120 | M1 | A single night calculation may be embedded in a calculation for a number of nights other than 5 or 2 different numbers provided not ‘× a’ for single and ‘× 2a’ for the twin rooms |
| (£) 9600 | A1 | CAO |
| (Total cost of the 8 nights is 7337.52 + 9600 =) (£) 16937.52 | B1 | FT adding ‘their derived perceived final costs’ provided at least 4 marks previously awarded |
| Organisation and communication | OC1 | For OC1, candidates will be expected to:
|
| Writing | W1 | For W1, candidates will be expected to:
|
| Scheme | Marks | Comments |
|---|---|---|
| (Number of litres of fuel) (33860 – 32474) ÷ 4 | M2 | M1 for (km travelled) 33860 – 32474 (= 1386) |
| = 346.5 (litres) | A1 | Allow rounded to 347 or truncated to 346, provided not from incorrect working, including from trial and improvement, May be implied in later work If M0 A0, award SC1 for any one of the following:
|
| (Cost of fuel) 346.5 × 1(.)86 | M1 | FT ‘their number of litres of fuel’ |
| (£)644.49 or 64449(p) | A1 | CAO. If units are given, they must be correct |
Alternative
3(b) Alternative method:
| Scheme | Marks | Comments |
|---|---|---|
| (Fuel cost per km) 1(.)86 ÷ 4 | M1 | |
| = 46.5 (p/km) or 0.465 (£/km) | A1 | Allow rounded to (0.)47 or truncated to (0.)46 |
| (Distance travelled 33860 – 32474 =) 1386 (km) | B1 | |
| (Cost of fuel) 1386 × 0.465 or 1386 × 46.5 | M1 | FT 1386 × ‘their derived 46.5’ or 1386 × ‘their derived 0.465’ OR FT ‘their 1386’ × ‘their 1(.)86 ÷ 4’, including use of 33860, 32474 and 33860 + 32474 |
| (£)644.49 or 64449(p) | A1 | CAO. If units are given, they must be correct |