Foundation June 2018 Paper 3 Q12
12 A takeaway sells 10-inch pizzas and 12-inch pizzas.
Here is some information about the numbers sold in two weeks.
Week 1
| 10-inch | 512 |
| 12-inch | 231 |
| Total | 743 |
Week 2
(a) In each week a proportion of the pizzas sold were 10-inch.
In which week was this proportion greater?
Show working to support your answer. [2 marks]
(b) The table shows the profit or loss the takeaway makes on each pizza.
| Normal price | Offer price | |
|---|---|---|
| 10-inch | £3.74 profit | 51p loss |
| 12-inch | £5.29 profit | 4p loss |
In week 1 the total profit was £1895.55
At the end of week 1 the takeaway spent £175 on adverts.
Was the increase in profit in week 2 more than the cost of the adverts?
You must show your working. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(512 \div 743\) or 0.6 or 0.68… or 0.69 or \(758 \div 1065\) or 0.7 or 0.71… | M1 | oe |
| 0.6 or 0.68… or 0.69 and 0.7 or 0.71… and Week 2 | A1 | |
| Alternative method 2 | ||
| \(512 \div 231\) or 2.2 or 2.21… or 2.22 or \(758 \div 307\) or 2.4 or 2.46… or 2.47 or 2.5 | M1 | oe |
| 2.2 or 2.21… or 2.22 and 2.4 or 2.46… or 2.47 or 2.5 and Week 2 | A1 | |
| Alternative method 3 | ||
| \(\dfrac{512}{743}\) or \(\dfrac{758}{1065}\) | M1 | \(\dfrac{512}{231}\) or \(\dfrac{758}{307}\) |
| \(\dfrac{545280}{791295}\) and \(\dfrac{563194}{791295}\) and Week 2 | A1 | \(\dfrac{157184}{70917}\) and \(\dfrac{175098}{70917}\) and Week 2 |
Additional guidance
| Accept working in percentages | |
| Proportions can be calculated using reciprocals in both Alternative method 1 and Alternative method 2 eg \(231 \div 512\) | |
| 60(%) or 68(%) or 69(%) or 70(%) or 71(%) | M1 |
| (10% = 74.3 followed by) \(\dfrac{512}{74.3} \times 10\) or (10% = 106.5 followed by) \(\dfrac{758}{106.5} \times 10\) is oe for Alternative method 1 | M1 |
| Answer | Mark | Comments |
|---|---|---|
| \(396 \times 3.74\) or 1481.04 or \(164 \times 5.29\) or 867.56 or \(362 \times 0.51\) or 184.62 or \(143 \times 0.04\) or 5.72 | M1 | oe Week 2 profit on 10-inch pizzas Week 2 profit on 12-inch pizzas Week 2 loss on 10-inch pizzas Week 2 loss on 12-inch pizzas |
| their 1481.04 + their 867.56 or 2348.6(0) or their 184.62 + their 5.72 or 190.34 or their \(1481.04 -\) their 184.62 or 1296.42 or their \(867.56 -\) their 5.72 or 861.84 | M1dep | oe Week 2 profit for both pizzas Week 2 loss for both pizzas Week 2 profit – loss on 10-inch pizzas Week 2 profit – loss on 12-inch pizzas |
| their \(2348.6(0) -\) their 190.34 or their 1296.42 + their 861.84 or 2158.26 | M1dep | Total week 2 profit from total profit – total loss |
| (£)87.71 or (£)262.71 and Yes or (£)1983.26 and Yes or (£) 2158.26 and (£)2070.55 and Yes | A1 | Total week 2 profit – (total week 1 profit + cost of adverts) Total week 2 profit – total week 1 profit Total week 2 profit – cost of adverts Condone eg £87.71p |
Additional guidance
| Accept use of inequality sign or words to imply “Yes” in final answer | |
| Accept –184.62 and –5.72 for first M1 | |
| Accept working in pence to calculate losses for M1 | |
| 2070.55 is total week 1 profit + cost of adverts | |
| Answer of (£)87.71 does not require “Yes” to be stated as the advert cost has been subtracted | M1M1M1A1 |