Question

Three numbers X, Y, and Z are in the ratio 2:7:8. If 12 is subtracted from Y, then three numbers form a geometric sequence (in the order X, Y–12, Z). Find X, Y, and Z. There are 2 sets.

Answer 1

(X, Y, Z) = (8, 28, 32)

Explanation:

The ratio units will form a geometric sequence if the middle one is the square root of the first and last:

Y' = √(2·8) = 4

To get this value from 7, we must subtract 3. In the real sequence we must subtract 12, so each "ratio unit" must stand for 12/3 = 4 real units, and the real numbers X, Y, Z are 2·4 = 8, 7·4 = 28, 8·4 = 32.

(X, Y, Z) = (8, 28, 32)

(X, Y-12, Z) = (8, 16, 32) . . . . a geometric sequence with a ratio of 2