Higher June 2017 Paper 1 Q18
18 Bottles of drink are for sale at three shops.
The normal price of a bottle is the same at each shop.
| Shop A Buy 1 bottle Get 2 more bottles at half price | Shop B Buy 2 bottles Get 3 more bottles at half price | Shop C 30% off a bottle |
What is the cheapest way to buy exactly 8 bottles?
You can buy from more than one shop.
You must show your working. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 – price for 8 bottles | ||
| Any two (including at least one combination) of Single shops Method to work out cost using one shop Shop A \(3 \times 1 + 5 \times 0.5\) or 5.5 or \(4 \times 1 + 4 \times 0.5\) or 6 or Shop B \(4 \times 1 + 4 \times 0.5\) or 6 or \(5 \times 1 + 3 \times 0.5\) or 6.5 or Shop C \(8 \times 0.7\) or 5.6 Combinations Method to work out cost using two shops A and B \((1 + 2 \times 0.5) + (2 \times 1 + 3 \times 0.5)\) or 5.5 or B and C \((2 \times 1 + 3 \times 0.5) + (3 \times 0.7)\) or 5.6 or A and C \((2 \times 1 + 4 \times 0.5) + (2 \times 0.7)\) or 5.4 or \((1 \times 1 + 2 \times 0.5) + (5 \times 0.7)\) or 5.5 | M2 | oe Values may be in £ throughout M1 for any one single shop or combination |
| 6 bottles from A and 2 bottles from C with M2 awarded | A1 | Condone 2 from A and 2 from C with M2 awarded SC2 6 bottles from A and 2 bottles from C with M1M0 awarded SC1 6 bottles from A and 2 bottles from C with M0M0 awarded |
| Alternative method 2 – best average cost per bottle | ||
| A is \(\dfrac{2}{3}\) or B is 0.7 or C is 0.7 | M1 | Accept 0.66 or 66(p) or better truncation or rounding or 0.67 or 67(p) |
| A is \(\dfrac{2}{3}\) and B is 0.7 and C is 0.7 | M1 | |
| 6 bottles from A and 2 bottles from C with M2 awarded | A1 | Condone 2 from A and 2 from C with M2 awarded SC2 6 bottles from A and 2 bottles from C with M1M0 awarded SC1 6 bottles from A and 2 bottles from C with M0M0 awarded |
Additional guidance
| In both methods, if a price or variable is chosen, values would be the respective multiples of that price or variable | |
| For SC2, the M1 may have been awarded for the correct method or price for a different selection of 8 bottles or for the 6 from A and 2 from C eg only working is 6 from A and 2 from C and £5.40 | SC2 |
| Calculations or total costs may not be labelled, but shops may be implied by prices | |
| An incorrect evaluation of the total cost of 6 from A and 2 from C leads to a maximum of M1M1A0 Ignore other incorrect evaluations which do not affect the award of marks |