Question

£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 1

£90

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.