June 2018 Paper 1 Q4
4 \(P = 4x \quad\) and \(\quad Q = 7x\)
\(P\) increases by 25%
\(Q\) decreases by 40%
Now, \(P\) is 28 greater than \(Q\).
Work out the value of \(x\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(1.25 \times 4x\) or \(5x\) | M1 | oe |
| \(0.6 \times 7x\) or \(4.2x\) | M1 | oe |
| their \(5x\) − their \(4.2x = 28\) or \(0.8x = 28\) | M1dep | oe eg their \(5x\) = their \(4.2x + 28\) dep upon at least one of previous M marks earned |
| \(x = 35\) | A1 | |
| Alternative method 2 | ||
| two numbers in the ratio 4 : 7 | M1 | |
| correct increase by 25% and decrease by 40% calculations and comparison with 28 | M1dep | If difference is not 28, then first numbers must be clearly rejected |
| second trial with correct calculations and comparison | M1dep | correct first trial means 2nd and 3rd M marks scored automatically |
| \(x = 35\) | A1 | |
Additional guidance
| Mark the better of their two versions if they try both methods. | |
| In alt 2 … for the 2nd M1 (dep on 1st M1) … the % calculations must be correct. If the difference is not 28 they must reject them. Attempting another two % calculations is sufficient evidence of this. | |
| In alt 2 … for the 3rd M1 (dep on the first two M1’s) … the difference must be closer than their first attempt. They can have more than one attempt at this so as to eventually score the 3rd M1. To score this mark they need to indicate clearly that this further attempt is better than their first attempt. | |
| In alt 2 … if it isn’t clear in which order they have done their attempts (eg very untidy working written all over the page) and they do not indicate which is the better attempt, then they can score a maximum of 2 marks. |