Math
posted by Ruby .
Mrs Li bought some oranges. She gave 1/2 of them to her sister, 1/4 of the remainder to her neighbour, 3/5 of those left to her children and had 6 left in the end. How many oranges did Mrs Li buy? Explain your workings

If she had 6 left after giving 3/5 to her children, she had 6/(2/5) = 15 to start.
If she had 15 left after giving 1/4 to her neighbors, she had 15/(3/4) = 20 to start.
If she had 20 left after giving 1/2 to her sister, she had 20/(1/2) = 40 to start out with in the first place.
Check:
40  20 = 20
20  5 = 15
15  9 = 6
Everybody is happy.
Alternatively:
X  X/2 = X/2
X/2  (X/2)(2/5) = 3X/8
3X/8  (3X/8)(3/5) = 6X/40 = 6
6X = 240 or X = 40.