History of Hindu Mathematics: A Source Book v2.c17.s12.8

v2.c17.s12.8

If x, y, z represent the prices of a ruby, sapphire and pearl respectively, then by the question $5x + 8y + 7z + 90 = 7x + 9y + 6z + 62.$ Therefore $x = (-y + z + 28)/2.$ Assume z = 1; then $x = (-y + 29)/2,$ whence by the method of the pulveriser, we get $x = 14 - m, y = 2m + 1,$ where m is an arbitrary integer. Putting m = 0, 1, 2, 3, we get the values of (x, y, z) as (14, 1, 1), (13, 3, 1), (12, 5, 1), (11, 7, 1), etc. Bhâskara II then observes, “By virtue of a variety of assumptions multiplicity of values may thus be obtained.”