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kozerog [31]
3 years ago
9

£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?
Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
3 0

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.

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