## 279. Math Puzzle $8 / 88$

Four people give the following information:

1. Person: "I am $5 \mathrm{~kg}$ lighter than the third person."
2. Person: "I weigh half of what the first and fourth person together weigh."
3. Person: "The fourth person is $29 \mathrm{~kg}$ lighter than I am."
4. Person: "My mass is one quarter of the total mass of the first, second, and third person."

Can the four people ride in an elevator with a load capacity of $350 \mathrm{~kg}$?
Let's denote the four people in sequence as $a, b, c$, and $d$, then the following equations arise:

$$
\begin{aligned}
a & =c-5=d+24 \\
b & =\frac{a+d}{2}=d+12 \\
c & =d+29 \\
d & =\frac{a+b+c}{4} \\
4 d & =(d+24)+(d+12)+(d+29) \quad, \quad d=65 \text{ kg}
\end{aligned}
$$

From this, it follows that: $a=86 \text{ kg}, b=77 \text{ kg}, c=94 \text{ kg}$. Together, the people weigh $325 \text{ kg}$. Therefore, they are allowed to use the elevator, which is rated for $350 \text{ kg}$.