a is x % of b, b is x% more than a. Find x

Let y = x/100 (so x% = y).

1. From "a is x% of b": a = y·b.

2. From "b is x% more than a": b = a(1 + y).

3. Substitute a = y·b into b = a(1 + y): b = (y·b)(1 + y). Divide both sides by b (b ≠ 0): 1 = y(1 + y).

4. Rearrange to form a quadratic: y^2 + y - 1 = 0. Solve for y: y = (−1 ± sqrt(1 + 4))/2 = (−1 ± sqrt(5))/2. Take the positive root: y = (sqrt(5) − 1)/2 ≈ 0.618034.

5. Convert back to percent: x = 100·y = 100·(sqrt(5) − 1)/2 ≈ 61.8034%, which is approximately 61.8% (rounded to 62%).

Answer: approximately 61.8% (≈ 62%).

Note: The value 0.618... is related to the golden ratio; its reciprocal is (1 + sqrt(5))/2 ≈ 1.618.