$72.80
Let's create a series of equations to express what we know. I'll use the variables A,B,C to represent respectively Alex's, Ben's and Carl's money.
"If Alex gives $4.55 to Ben, the two boys will have an equal amount of money."
A - 4.55 = B + 4.55
"If Ben gives $4.55 to Alex, Alex will have 3 times as much money as Ben.
A + 4.55 = (B - 4.55)*3
Carls amount of money is the sum of the two other boys' money. How much do the three boys have in all?
C = A + B
Let's take the 1st equation and solve for A
A - 4.55 = B + 4.55
A = B + 4.55 + 4.55
A = B + 9.10
Now let's take the 2nd equation and substitute (B+9.10) for A and then solve for B.
A + 4.55 = (B - 4.55)*3
(B+9.10) + 4.55 = (B - 4.55)*3
B + 9.10 + 4.55 = 3B - 3*4.55
B + 13.65 = 3B - 13.65
13.65 = 2B - 13.65
13.65 + 13.65 = 2B
2*13.65 = 2B
13.65 = B
So Ben has 13.65. Let's use that to calculate Alex's money.
A = B + 9.10
A = 13.65 + 9.10
A = 22.75
And now we know that Alex has 22.75, let's use that and Ben's amount to calculate Carl's
C = A + B
C = 22.75 + 13.65
C = 36.40
So Alex has $22.75, Ben has $13.65, and Carl has $36.40. Since we're looking for the total amount of money the boys have, that is:
$22.75 + $13.65 + $36.40 = $72.80
