Math

A king couldn't sleep so, he devoured 1/6 of a bowl of mangoes. Later, the queen got hungry and took 1/5 of the bowl of mangoes. The prince awoke and ate 1/4 of the bowl of mangoes. After, he came back and ate another 1/3. Obviously, he was hungry and ate another 1/2. 3 mangoes were left for the servants. How many mangoes were in the bowl before the king, queen, and prince ate mangoes?

I need help solving this. Explain. Thank you! (;

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  1. let the number of original mangoes be x
    King ate 1/6, so (5/6)x are left
    Queen ate 1/5 of that so (4/5)(5/6)x are left
    prince ate 1/4 of that so (3/4)(4/5)(5/6)x are left
    prince then ate 1/3 of that leaving (2/3)(3/4)(4/5)(5/6)x
    prince then ate 1/2 of that, leaving
    (1/2)(2/3)(3/4)(4/5)(5/6)x

    this cancels very nicely to (1/6)x

    but we know (1/6)x = 3
    so x = 18

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