If we forget about the £150 more for a second then we can think of some very basic scenarios where the 5 : 2 ratio is satisfied. For example, Jon has £5 Nik has £2 or Jon has £10 Nik has £4 and so on. From this information we can set up an equation to find what Nik has if Jon has say £100. What is that equation? we let J represent how much Jon has and N represent how much Nik has then we can say2J = 5N and this comes directly from the ratio given.Now we consider the £150 more that Jon gets and we can set up another equationJ = N + 150 if Nik got £150 more then they'd have the same.So now we have 2 equations and two variables and we can solve it like they're simultaneous equations. There are a couple of methods for solving simultaneous equations but in this case the method to use is obvious, substitution. We use substitution because our second equation J = N + 150 is already in terms of J so we can just substitute it in to the first equation. By doing this we get2(N + 150) = 5N now we expand the brackets2N + 300 = 5N take N on to one side300 = 3N make N the subjectN = 100 we have an equation to find what J is if N is 100, 2J = 5N2J = 5(100) make J the subjectJ = 250
