Question 956857
J=James' money; S=sister's money; B=brother's money
Take each line and try to extract all the information
This morning James had half as much money as his sister and 27 dollars less than his brother.
J=(1/2)S=B-27
After the payoff, James's brother has twice as much money as James's sister. How much money does James have now
B+12=2(S-24)
Look for ways to substitute for variables to wind up with only one variable in the equation. We can substitute for B and S in terms of J:J=B-27 so B=J+27:
(J+27)+12=2(S-24) 
And for S:J=(1/2)S so S=2J
J+39=2(2J-24)
J+39=4J-48 Add 48 to each side.
J+87=4J Subtract J from each side.
87=3J Divide each side by 3
29=J ANSWER 1: James started with $29. So now James has $29+$12=$41.
CHECK:
B=J+27=29+27=$56 Brother started with $56
S=2J=2($29)=$58 Sister started with $58
B+$12=2(S-$24)
$56+$12=2($58-$24)
$68=2($34)
$68=$68