7.2. Problem 33 of the Rhind papyrus asks for a quantity that yields 37 when inc

Question

7.2. Problem 33 of the Rhind papyrus asks for a quantity that yields 37 when increased by its two parts (two-thirds), its half, and its seventh part. Try to get the author's answer The quantity is 16 56 679 776. Hin: The table for doubling fractions gives the last three terms of this expression as the double of 97. The scribe first tried the number 16 and found that the result of these operations applied to 16 fell short of 37 by the double of 42, which, as it happens, is exactly 1 3 2 7 times the double of 97.]

Explanation / Answer

suppose the quantity is x, so

x + x(2/3) + x(1/2) + x(1/7) = 37

x(1+2/3+1/2+1/7)=37

Restated, divide 37 by 1 +2/3 + 1/2 + 1/7

1 1 + 1/3 + 1/6 + 1/18 2 3 + 1/9 4 6 + 1/6 + 1/18

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