Foundation November 2017 Paper 1 Q22
22
\(x : y \;=\; 7 : 4\)
\(x + y \;=\; 88\)
Work out the value of \(\quad x - y\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(88 \div (7 + 4)\) or \(88 \div 11\) or 8 | M1 | oe \(11 \times 8 = 88\) |
| their \(8 \times 7\) and their \(8 \times 4\) or their \(8 \times 7\) and \(88 -\) their value or their \(8 \times 4\) and \(88 -\) their value or 56 and 32 or their \(8 \times (7 - 4)\) or their \(8 \times 3\) | M1dep | oe eg \(8 \times 7 = 63\) and \(88 - 63\) eg \(8 \times 4 = 30\) and \(88 - 30\) |
| 24 | A1 | |
| Alternative method 2 | ||
| One correctly evaluated trial for two numbers, other than 7 and 4, in the ratio 7 : 4 | M1 | eg \(70 + 40 = 110\) |
| 56 and 32 | M1dep | eg \(56 + 32 = 88\) |
| 24 | A1 | |
| Alternative method 3 using \(x : y = 7 : 4\) (correct) | ||
| \(4x = 7y\) and \(4x + 4y = 352\) or \(4x = 7y\) and \(7x + 7y = 616\) | M1 | oe forming equation from ratio and equating coefficients |
| \(11y = 352\) or \(y = 32\) or \(11x = 616\) or \(x = 56\) | M1dep | oe equation in one variable |
| 24 | A1 | |
| Alternative method 4 using \(x : y = 4 : 7\) (incorrect) | ||
| \(7x = 4y\) and \(4x + 4y = 352\) or \(7x = 4y\) and \(7x + 7y = 616\) | M1 | oe forming equation from ratio and equating coefficients |
| \(11x = 352\) or \(x = 32\) or \(11y = 616\) or \(y = 56\) | M1dep | oe equation in one variable |
| their answer | A0 | |
| Alternative method 5 using \(x : y = 7 : 4\) (correct) | ||
| \(x = \dfrac{7}{4}y\) or \(y = \dfrac{4}{7}x\) or \(x = 88 - y\) or \(y = 88 - x\) | M1 | oe making one variable the subject |
| \(\dfrac{7y}{4} + y = 88\) or \(\dfrac{11}{4}y = 88\) or \(x + \dfrac{4}{7}x = 88\) or \(\dfrac{11}{7}x = 88\) | M1dep | oe equation in one variable |
| 24 | A1 | |
| Alternative method 6 using \(x : y = 4 : 7\) (incorrect) | ||
| \(y = \dfrac{7}{4}x\) or \(x = \dfrac{4}{7}y\) or \(x = 88 - y\) or \(y = 88 - x\) | M1 | oe making one variable the subject |
| \(\dfrac{7}{4}x + x = 88\) or \(\dfrac{11}{4}x = 88\) or \(y + \dfrac{4}{7}y = 88\) or \(\dfrac{11}{7}y = 88\) | M1dep | oe equation in one variable |
| their answer | A0 | |
Additional guidance
| –24, with no incorrect working, implies 56 and 32 | M1M1A0 |
| \(x = 32\) and \(y = 56\) | M1M1A0 |