# Math

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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

• Math -

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.

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