Higher Paper 2

\begin{aligned} &\text{Initial ratio A:B:C }=4:5:3.\; \text{Ben has £150 }\Rightarrow\; \text{one part }=£30.\\ &\text{So initially } A=£120,\; B=£150,\; C=£90.\\ &\text{After transfers } p \text{ to Ben and } q \text{ to Carla: } 120-(p+q):150+p:90+q = 3:6:4.\\ &\text{Let } 120-(p+q)=3k,\; 150+p=6k,\; 90+q=4k.\\ &\Rightarrow\; p=6k-150,\; q=4k-90.\\ &\text{Substitute: } 120-(6k-150)-(4k-90)=3k \Rightarrow 360-10k=3k \Rightarrow k=\tfrac{360}{13}.\\ &\therefore\; q=4k-90=\tfrac{270}{13}\approx 20.77.\\ &\text{Anna gave £20.77 to Carla (exactly } £\tfrac{270}{13}\text{).} \end{aligned}