To solve this problem, let us say that:
x = money of brother # 1
y = money of brother # 2
The sum is $55 therefore:
x + y = 55 ---> equation 1
Further, we know that one of the brothers has 15 more money than the other, let us say that:
x = y + 15 ---> equation 2
Combining equations 1 and 2 to find for the value of y:
(y + 15) + y = 55
2y = 40
y = 20
Calculating for x from equation 2:
x = 20 + 15
x = 35
Therefore each has saved $20 and $35.