£150 is divided between Malachy, Paul & Brian so that Malachy gets twice as much as Paul, and Paul gets three times as much as Brian. How much does Malachy get?

Answer:£90 Step-by-step explanation: Let M = Malachy's share and P = Paul's share and B = Brian's share. We have three conditions:                                               (1)               M = 2P                                                (2)                P = 3B                                                (3)   M + P + B = 150 Solve for B: Substitute (2) into (3)             (4) M + 3B + B = 150                                                (5)       M + 4B = 150 Substitute (2) into (1)                                  M = 2(3B)                                                (6)                M = 6B Substitute (6) into (5)                6B + 3B + B = 1 50                                                (7)                B = 15 Solve for P: Substitute (7) into (2)                                  P = 3×15                                                (8)                P = 45 Solve for M:Substitute (8) into (1)                                  M = 2×45                                                                    M = 90 Malachy gets £90.