£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?

£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.