2015 · Q2
If 37/13 = 2 + 1/(x + 1/(y + 1/z)) where x, y, z are natural numbers, then what is z equal to?
Elementary MathematicsAlgebra
- A1
- B2
- C3
- DCannot be determined due to insufficient data
Explanation
37/13 = 2 + 11/13 = 2 + 1/(13/11) = 2 + 1/(1 + 2/11) = 2 + 1/(1 + 1/(11/2)) = 2 + 1/(1 + 1/(5 + 1/2)). Comparing with 2 + 1/(x + 1/(y + 1/z)) gives x = 1, y = 5, z = 2, so z = 2 (option B).