Homework Egyptian problem

Adam gave Sam 45 dollars to buy groceries. He requires that the number of apples should be three times the number of bananas. The number of bananas should be double the number of oranges. suppose apples cost 2 dollars and bananas cost 1 dollar, and oranges cost 1 dollar, how many of each fruit should he buy?

modern solution: 

let the number of oranges be x. 

x +2x+6x*2=45

15x=45

x=3


false position method:

let x be 2 

2+4+6*2*2=30

we need 45, which is 45/30=1+1/2 as big, so x must be 2 times 1+1/2 , which is 2+1=3

check: if x=3, x +2x+6x*2=45




评论

  1. Susan Gerofsky2020年11月11日 17:46

    Good problem and explanation. One thing that you might think about is that ancient Egyptians mostly used the method of false position as a way of working with fractions and unknown quantities. It works fine with whole number quantities too as you've done it here, but I'm not sure if they would have solved it that way.

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