Numeracy Intermediate June 2017 Unit 1 Q4
4. Lazar wants to send a package to Germany.
He looks at pricing charts for three different companies, ParcelMax, DirectGo and Pack2save.
ParcelMax
Total cost =
Sum of the 3 dimensions in cm × £0.60
DirectGo
Total cost =
Volume measured in cm3 × £0.01
Pack2save
Total cost =
Total area of all 6 faces measured in cm2 × £0.02
Lazar’s parcel is a cuboid measuring 10 cm by 20 cm by 30 cm.
Diagram not drawn to scale
(a) Find the cost of sending the parcel for each of the three different companies.
Give each of your answers in pounds (£).
Give each of your answers in pounds (£).
(i) ParcelMax [2]
(ii) DirectGo [3]
(iii) Pack2save [4]
(b) What is the percentage saving that Lazar will make by choosing the cheapest option rather than the most expensive option? [2]
| Scheme | Marks | Comments |
|---|---|---|
| (i) (10 + 20 + 30) × 0.6 or 60 × 0.6 or (10 + 20 + 30) × 60 ÷ 100 | M1 | Allow intention of brackets i.e. 10 + 20 + 30 × 0.6 |
| (£)36 | A1 | CAO and must be from correct working If no marks, award SC1 for an answer of 3600(p), not for £3600 |
| (ii) 10 × 20 × 30 (= 6000) | M1 | An answer of £6000 implies M1 only |
| × 0.01 or (× 1) ÷ 100 | m1 | Depends on previous M1 Award of m1 implies previous M1 |
| (£)60 | A1 | CAO If M1 m0 A0 also award SC1 for an answer of 6000p |
| (iii) 2× {(10×20) + (20×30) + (10×30) (= 2200) | M2 | M1 for sight of sum of at least 2 of the 6 possible products: 10×20, 20×30, 10×30 |
| × 0.02 or × 2 ÷ 100 | m1 | Depends on M2 or M1 previously awarded |
| (£)44 | A1 | CAO If M2 m0 A0, also award SC1 for an answer of 4400(p), not for £4400 |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{60 - 36}{60}\) (×100) | M1 | Strict FT ‘their most expensive’ and ‘their cheapest’ |
| 40 (%) | A1 | If FT is not a whole number, then accept rounded or truncated to a whole number If no marks, award SC1 for an answer of 60(%) from 36/60 or \(\dfrac{\text{‘their cheapest’}}{\text{‘their most expensive’}}\) expressed correctly as a percentage |