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This morning James had half as much money as his brother and 27 dollars less than his sister. Then his brother paid James and his sister each 12 dollars to wash his car. After the payoff, James's sister has twice as much money as James's brother. How much money does James have now?

For a question like this, it is essential that you explain carefully to your reader what any variable that you introduce represents. Begin your solution by introducing some variable or variables and tell the reader exactly what they represent.
 

Btw, THERE IS a similar question, but it is some twisted and distorted version of this. Don't send me that link, please.

 Feb 3, 2019
 #1
avatar+18492 
+2

b = brother's money    

     s = sister's money

             then    j = james'  money = 1/2 b = s-27  

                                                           b= 2s-54              (1)             this is given.

 

AFTER the car wash

b-12-12 =b-24  is brother's money balance         and     s+12 is sister's new balance    and    j = (s-27) +12

AND

 

b-24 = 1/2 (s+12)        given

Substitute equation (1) in for b

 

2s-54 -24 = 1/2(s+12)

3/2 s = 84

s = 56   originally             James money  after carwash   = (s-27) +12 = 41 dollars

 Feb 3, 2019
 #2
avatar
+1

Let what the brother started with=B
Let what his sister had =S
Then James had =1/2B   and S -27 than his sister.
James gets =1/2B + 12
Sister gets = S + 12
James's brother has left= B - 24
S + 12 =2(B - 24) 

1/2B + 12 =S - 27 + 12, solve for B, S

                                                                              
B =$58 - what the brother started with
S =$56 - what the sister started with.


James has now: $56 - 27 + 12 = $41

 Feb 3, 2019
 #3
avatar+101871 
+1

Let James money = x

Let his sister's money  x + 27

Let his brother's money = 2x

 

After the payoff....

James brother has 2x - 24

And James sister has   x + 27 + 12  =  x + 39

 

So

 

x + 39 =  2 [ 2x - 24 ]

 

x + 39 = 4x - 48

 

87 = 3x

 

x = 29

 

So

 

James has  29 + 12   = $41

 

 

cool cool cool

 Feb 3, 2019

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