1MA0 Foundation November 2012 Paper 1 Q20
20 Sapir buys 60 bags.
She pays £3 for each bag.
Sapir sells \(\frac{1}{2}\) of the bags for £5 each.
She sells \(\frac{1}{3}\) of the bags for £4 each.
Sapir wants to make a total profit of £75
How much should she sell each of the remaining bags for? (4)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(\frac{1}{2} \times 60 = 30\), \(30 \times 5 = 150\) \(\frac{1}{3} \times 60 = 20\), \(20 \times 4 =\) £80 \(3 \times 60 = 180\) \(180 + 75 - 150 - 80 =\) £25 10 bags (i.e. \(60 - 30 - 20\)) sold for 25 \(25 \div 10 = 2.50\) OR \(\frac{1}{2} \times 60 = 30\), \(30 \times\) £2 = £60 profit \(\frac{1}{3} \times 60 = 20\), \(20 \times\) £1 = £20 profit \(60 + 20 =\) £80 \(80 - 75 = 5\) loss on 10 bags (i.e. \(60 - 30 - 20\)) \(10 \times\) £3 = £30 \(30 - 5 =\) £25 £\(25 \div 10 =\) £2.50 | 2.50 | 4 | M1 for \(\frac{1}{2} \times 60 \times 5\) (=150) or \(\frac{1}{3} \times 60 \times 4\) (=80) M1 (dep on 1st M1) for \(3 \times 60 + 75 - \text{`}150\text{'} - \text{`}80\text{'}\) oe (=25) M1 (dep on previous M1) for \(\text{`}25\text{'} \div (60 - \text{`}30\text{'} - \text{`}20\text{'})\) A1 for 2.50 (accept 2.5) OR M1 for \(\frac{1}{2} \times 60 \times 2\) (=60) or \(\frac{1}{3} \times 60 \times 1\) (=20) M1 (dep on 1st M1) for \((60 - \text{`}30\text{'} - \text{`}20\text{'}) \times 3 - (\text{`}60\text{'} + \text{`}20\text{'} - 75)\) oe (=25) M1 (dep on previous M1) for \(\text{`}25\text{'} \div (60 - \text{`}30\text{'} - \text{`}20\text{'})\) A1 for 2.50 (accept 2.5) |