Maths question! linear equation! help!

divide 1380 (it is sum of money!) among Ahmed John and Babita so that amount ahemed receives is 5 times as much as babitas share and is 3 times as much as johns share!! answers is 180 900 300!
helppppp

Let Babita's share = x
then Ahmad's share = 5x
John's share = 1/3 of 5x = 5x/3

The ratio of Ahmad, Babita and John's share = 5x : x : 5x/3
multiplying by 3 ==> 15x : 3x : 5x
Thus 15x +3x + 5x = 23 x = 1380
x = 1380/23 = 60

So, 15x = 15* 60 = 900
3 x = 3*60 = 180
5 x = 5*60 = 300

John receives j dollars.

Babita receives b dollars

Ahmed receives 5 times as much as Babita = 5b
Ahmed receives 3 times as much as John = 3j
5b = 3j
b = 3j/5
Babita receives 3/5 as much as John.

total distribution is 1380 dollars
j + b + 5b = 1380
j + 6b = 1380
j + 6(3j/5) = 1380
j = 300
John receives 300 dollars.

b = (3/5)300 = 180
Babita receives 180 dollars

Ahmed receives 3 times as much as John
3×300 = 900
Ahmed receives 900 dollars

Let's think of it in terms of shares. Let Ahmed's share = X, then Babitas share is X/5 (because Ahmed gets 5 times as much) and John's share = X/3. The sum of these shares must be 1380 so:

X + X/5 + X/3 = 1380

X (1 + 1/5 + 1/3) = 1380

X ( 23/15 ) = 1380

X = 1380 (15/23)
X = 900 (Ahmed's Share)

X/5 = 180 (Babita's share)

X / 3 = 300 (John's share)

A = 5B = 3J. This tells us also that B = 3J/5. Add all in terms of John.....

3J + 3J/5 + J = 1380........simplify and multiply across by 5

23J = 1380 x 5

J = 60 x 5 = 300, and therefore B = 180 and A = 900