Sabrina gave Samantha as many dollars as Samantha started out with. Samantha then gave Sabrina back as much as Sabrina had left. Sabrina then gave Samantha as back as many dollars as Samantha had left, which left Sabrina broke and gave Samantha a total of $80.00. How much did Sabrina and Samantha have at the beginning of their exchange?

Asslamo 3laykom

sabrina started with 50$
samantha started with 30$

peace be upon you

I forgot to tell to list the steps u amde to solve

Asslamo 3laykom

do not worry sattia

it is easy start from the bottom to top :D

you did not tell me is the answer is right ;)

peace be upon you

yes it is right but I need u to list the steps

Asslamo 3laykom

you did not ask for that before , put it in an indepedant thread , LOL

any way it is easy as i told you

the first key for the answer is to start from the bottom to top

the second key is the total ammount of the money with both girls ( is they girls )

ok here we start

- when sabrina gave samantha as many dollars as Samantha had left, which left Sabrina broke that means each girl had 40$
before giving sabrina to samantha as many as she had left

- the upper step is what is the ammout that was with sabrina (40$) is the dobule of what she had before samatha gave here as many as she had left

- now sabrina had (20$) and samantha had (60$) the last step , samantha gave sabrina as many as she started with , that means samanth started with the half of (60$) that was (30$) -> so sabrina had started with (50$) ;)



peace be upon you

Salamo 3alaikom,

This riddle is very tricky. I solved with a 1st degree equation as follows:

First Suppose that Sabrina has "x" and Samantha has "y" amounts of money and the difference between "x" and "y" = "r"

Then Sabrina has "y+r" and Samantha has "y" ------- 1

Second Sabrina gave Samantha the same amount she started with then the resulting change would be as follows:
Sabrina has "r" and Samantha has "2y" -------------- 2

Third Samantha gave Sabrina again "r" amount of money, this results in the following change:
Sabrina has "2r" and Samantha has "2y-r" ------------ 3

Fourth Sabrina gave Samantha what she has and became broke, this means that 2r=2y-r and here is the trick in that riddle

2r=2y-r then 3r=2y ---------------------- 4

Since Sabrina gave Samantha 2r then Samantha has now 2y-r+2r ie has 2y+r= 80

By substitution from 4: 3r+r =80 then r=20 and y=30 and x=50

Then Sabrina originally had 50 $ and Samantha had 30 $.

I wouldn't have reached that step since this riddle is really tricky. I inspired the solution from Aljaber to be honest.

Salam.