You and a friend each have a collection of tokens

Question

You and a friend each have a collection of tokens. Initially, for every 8 tokens you had, your friend had 3. After you give half of your tokens to your friend, your friend now has 18 more tokens than you. Initially, how many more tokens did you have than your friend?

Answer 1

Let N be the total number of tokens.

 

At the beginning, you have 8/11*N and your friend has 3/11*N <--- 8 to 3 ratio

 

You give half of your tokens to your friend: (1/2)(8/11)N = (4/11)N

 

You now have: (8/11)N - (4/11)N = (4/11)N

 

Your friend now has (3/11)N + (4/11)N = (7/11)N

 

The difference is 18.

 

(4/11)N + 18 = (7/11)N

 

18 = (7/11)N - (4/11)N

 

18  = (3/11)N

 

(18*11)/3 = n

 

n = 66

 

At the beginning, you have (8/11)*66 = 8*6 = 48

 and your friend has (3/11)*66 = 3*6 = 18

 

Half of yours is 24.

 

After you give half away, you have 48-24 = 24 and your friend has 18+24 = 42,

which is 42-24=18 more

 

So in the beginning , you had 48-18 = 30 more

 

 

Answer 2

Y for ”your tokens”, and F for friend’s

Y/F=8/3

Y-Y/2=F-18 or Y/2=F-18

solve this sustem of eqution.