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3. Model (
    767 [p][u u u u u]    (red + green)
    239 [p][u]            (red + blue)

Note: The parts p is for red and units u is for green and blue.
Clearly 5u - u = 767 - 239
             u = 132
Number of red beads = p = 239 - u = 239 - 132 = 107.


4. Since the money is going to be cut into quarters (1/4) and fifths (2/5),
the natural thing to do is to use LCM(4,5) = 20 as the units.

So she started with 20u.
 1/4 to 1st child  = 5u
 2/5 to 2nd child  = 8u
 rest to 3rd child = 20u - 5u - 8u = 7u = 280
Thus u = 280/7 = 40.
She gave 20u = 20 x 40 = $800 to the children.

 

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