Higher June 2019 Paper 3 Q21
21 Hanif makes green paint by mixing blue paint and yellow paint in the ratio
blue : yellow = 7 : 3
He buys blue paint in 50-litre containers, each costing £225
He buys yellow paint in 20-litre containers, each costing £80
He wants to
sell the green paint in 5-litre tins
make 40% profit on each tin.
How much should he sell each tin for? [5 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 – making 10 litres of paint | ||
| \(225 \div 50\ (= 4.5(0))\) or \(80 \div 20\ (= 4(.00))\) | M1 | cost of 1 litre for one colour |
| \(225 \div 50\ (= 4.5(0))\) and \(80 \div 20\ (= 4(.00))\) | M1 | cost of 1 litre for both colours |
| their \(4.5(0) \times 7 +\) their \(4(.00) \times 3\) or 43.5(0) | M1dep | 31.5(0) + 12(.00) dep on M2 |
| their \(43.5(0) \times 1.4\) or 60.9(0) or their \(43.5(0) \div 2 \times 1.4\) | M1dep | oe dep on M3 |
| 30.45 | A1 | |
| Alternative method 2 – making 5 litres of paint | ||
| \(5 \div (7 + 3)\) or 0.5 | M1 | |
| their \(0.5 \times 7\) or 3.5 and their \(0.5 \times 3\) or 1.5 | M1dep | 3.5 : 1.5 |
| \(\dfrac{\text{their } 3.5}{50} \times 225\) or 15.75 and \(\dfrac{\text{their } 1.5}{20} \times 80\) or 6 | M1dep | dep on M2 |
| (their 15.75 + their 6) \(\times\ 1.4\) | M1dep | oe \(21.75 \times 1.4\) or 21.75 + 8.7(0) dep on M3 |
| 30.45 | A1 | |
| Alternative method 3 – making 10 litres of paint when profit is added at the start | ||
| \(225 \times 1.4\ (= 315)\) and \(80 \times 1.4\ (= 112)\) | M1 | 40% added to the cost of both colours |
| their \(315 \div 50\ (= 6.3(0))\) or their \(112 \div 20\ (= 5.6(0))\) | M1dep | selling price of 1 litre of either colour |
| their \(315 \div 50\ (= 6.3(0))\) and their \(112 \div 20\ (= 5.6(0))\) | M1dep | selling price of 1 litre of both colours |
| their \(6.3(0) \times 7 +\) their \(5.6(0) \times 3\) or 60.9(0) | M1dep | oe 44.1(0) + 16.8(0) dep on M3 |
| 30.45 | A1 | |
| Alternative method 4 – making \(n\) litres of paint | ||
| \(225 \div 50 \times 0.7n\) or \(3.15n\) or \(80 \div 20 \times 0.3n\) or \(1.2n\) | M1 | cost of blue or yellow paint in \(n\) litres of green paint |
| \(225 \div 50 \times 0.7n\) or \(3.15n\) and \(80 \div 20 \times 0.3n\) or \(1.2n\) | M1 | cost of blue and yellow paint in \(n\) litres of green paint |
| their \(3.15n\) + their \(1.2n\) or \(4.35n\) | M1dep | total cost of \(n\) litres of green paint dep on M2 |
| their \(4.35n \times 1.4\) or \(6.09n\) | M1dep | oe dep on M3 |
| 30.45 | A1 | |
Additional guidance
| If the student attempts more than one method, mark each method and award the highest mark | |
| Alt 4 value of \(n\) must be clear eg 100 litres total or 700:300 (1000 litres implied) | |
| Alt 4 their \(4.35n \div \text{k} \times 1.4\) implies their \(4.35n \times 1.4\) where \(\div\,\text{k}\) is their attempt to scale to the cost of a 5-litre tin | M1M1M1M1 |