10. (10 points) A school's entrance exam has set a passing score. Among the students who took the exam, only $\frac{1}{4}$ were admitted. The average score of admitted students is 10 points higher than the passing score, while the average score of those not admitted is 26 points lower than the passing score. The average score of all candidates is 70 points. What is the passing score?
【Analysis】According to the problem, only $\frac{1}{4}$ of the students who applied were admitted. Assuming the number of students who applied is 4, only 1 person is admitted, and 3 people are not admitted. The total score is then $70 \times 4 = 280$ points. Using (total score of 4 people - the score by which the admitted person exceeds the admission line + the score by which the non-admitted persons fall short of the admission line) $\div 4$ gives the required result.

【Solution】The admission line is:
$$
\begin{aligned}
& (70 \times 4 - 10 + 26 \times 3) \div 4 \\
= & (280 - 10 + 78) \div 4 \\
= & 348 \div 4 \\
= & 87 \text { (points). }
\end{aligned}
$$

Answer: The admission line is 87 points.