Question

(Based on #6, p. 26, which comes from the Rhind Mathematical Papyrus, Problem 24)
Solve the following by the method of false position: A quantity and its 1/7 together become 190.

What is the quantity? (Be sure to demonstrate exactly how you are using the method of false position in your answer!)

Answer 1

We obtain the solution by the method of false position.

The equation we need to solve is,

First, guess that x=7, to obtain,

This guess is a good choice since it produces an integer value. However, 7 is not a solution to this problem as it gives a smaller value, that is, 8. Observe that  

Now, to compensate, multiply x (currently set to 7), by 95/4, and substitute again to get,

. Verifying, the solution is,

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