Suppose you give the older one x and the younger one y.
Since the initial amount was 100, it must be that x + y = 100.
The question states as follows:
(1/4)x - (1/3)y = 11
Multiply both sides by 12.
3x - 4y = 132.
Now just do the math.
x + y = 100
3x - 4y = 132.
Solving results in 7y = 168.
Thus y = 24, and x = 100 - y = 100 - 24 = 76.
Answer: 76 to the elder, 24 to the younger
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