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.
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
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
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