Question

£70 is divided between Natasha, Richard & Stephen so that Natasha gets twice as much as Richard, and Richard gets three times as much as Stephen. How much does Natasha get?

Answer 1

The share of Natasha is £ 42

Solution:

£70 is divided between Natasha, Richard & Stephen

Total amount = 70

Let the share of natasha be "x"

Let the share of richard be "y"

Let the share of stephen be "z"

Natasha gets twice as much as Richard

x = 2y ------ eqn 1

Richard gets three times as much as Stephen

y = 3z

$z = \frac{y}{3}$ ----- eqn 2

Total amount = 70

share of natasha + share of richard + share of stephen = 70

x + y + z = 70

Substitute eqn 1 and eqn 2

$2y + y + \frac{y}{3} = 70\\\\\frac{6y+3y+y}{3} = 70\\\\10y = 210\\\\y = 21$

Substitute y = 21 in eqn 1

x = 2y = 2(21) = 42

x = 42

Thus natasha gets £ 42