Higher November 2018 Paper 2 Q17
17 \(p\) and \(q\) are two numbers such that \(p \gt q\)
When you subtract 5 from \(p\) and subtract 5 from \(q\) the answers are in the ratio 5 : 1
When you add 20 to \(p\) and add 20 to \(q\) the answers are in the ratio 5 : 2
Find the ratio \(p : q\)
Give your answer in its simplest form. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 4 : 1 | P1 | for associating algebraic expressions with the correct ratio eg \(p - 5 : q - 5\ (= 5 : 1)\) or \(p + 20 : q + 20\ (= 5 : 2)\) |
| P1 | for \(\dfrac{p + 20}{q + 20} = \dfrac{5}{2}\) or \(\dfrac{p - 5}{q - 5} = \dfrac{5}{1}\) oe or \(p - 5 = 5(q - 5)\) or \(2(p + 20) = 5(q + 20)\) oe | |
| M1 | for a complete method shown to find \(p\) or \(q\) | |
| M1 | for a complete method shown to find \(p\) and \(q\) or two values for \(p\) and \(q\) that are in the ratio 4 : 1 or an unsimplified ratio 4 : 1 (eg 80 : 20) or an answer of 1 : 4 | |
| A1 | cao |
Additional guidance
Award for one of the two simultaneous equations
eg \(5q - p = 20\), \(5q - 2p = -60\) oe
Award for a simultaneous equation method to eliminate one variable leading to either \(p = 80\) or \(q = 20\)
Award for a simultaneous equation method to eliminate both variables leading to either \(p = 80\) and \(q = 20\)