Final answer:
By setting up a system of linear equations and solving for the variables, we find that Reuben has $23, Chang has $69, and Karen has $15.
Step-by-step explanation:
The question involves solving a system of linear equations to determine how much money Karen, Reuben, and Chang each have. Let's define the following variables: let R be the amount of money Reuben has, C be the amount Chang has, and K be the amount Karen has. According to the problem, Chang has 3 times what Reuben has (C = 3R), Karen has $8 less than Reuben (K = R - 8), and together they have $107 (R + C + K = 107).
To find out how much each person has, we set up the equations:
Substituting the expressions for C and K from equations 1 and 2 into equation 3, we get:
R + 3R + (R - 8) = 107
Combining like terms, we get:
5R - 8 = 107
Adding 8 to both sides, we get:
5R = 115
Dividing both sides by 5, we get:
R = 23
We can now determine the amounts for Chang and Karen:
C = 3R = 3(23) = $69
K = R - 8 = 23 - 8 = $15
Therefore, Reuben has $23, Chang has $69, and Karen has $15.