if 43/240<x1/x2<17/94, x3 is minimum possible value of x2 find 53*x3

Question

here x1 and x2 are positive integers

Answer 1

Question: if 43/240<x1/x2<17/94, x3 is minimum possible value of x2 find 53*x3

The difference between the two bounding values is 17/94 - 43/240 = 19/11280

We can rewrite the inequality as: 2021/11280 < x1/x2 < 2040/11280

Taking, for the moment, x2 = 11280,then we can write the inequality

2022 < x1 < 2039

Testing all values of x1 in the set [2022,2039], and cancelling out all factors in the quiotient of x1/x2, we find the quotient with the smallest denominator when x1 = 2032.

i.e. x1/x2 = 2032/11280 = 127/705, hence x3 = 705

Answer: 53*x3 = 37,365