MathNet 2025 — Part 01 (100 complete bilingual questions) Question 52

Determine the positive real numbers $a, b, c, d$ such that $a + b + c + d = 80$ and
$$
a + \frac{b}{1+a} + \frac{c}{1+a+b} + \frac{d}{1+a+b+c} = 8.
$$