(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!)
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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