£150 is divided between David, Mark & Henry so that David gets twice as much as Mark, and Mark gets three times as much as Henry. How much does David get?

David receives £90

Step-by-step explanation:

Let David's share be D

Let Mark's share be M

Let Henry's share be H

From the question, we obtained the following data:

David gets twice as much as Mark i.e

D = 2M

M = D/2

Mark gets three times as much as Henry i.e

M = 3H

H = M/3

H = (D/2) /3

H = D/6

The sum of their shares is £150 i.e

D + M + H = 150

D + D/2 + D/6 = 150

Multiply through by 6 to clear the fraction

6D + 3D + D = 900

10D = 900

Divide both side by the coefficient of D i.e 10

D = 900/10

D = 90

Therefore, David receives £90