Full solution

1 \times 8 + 8x = 9

Find

x

Identify Given Values: First, let's identify the given values and the unknown we need to find. We know that $336$ students were selected for the survey, $\frac{1}{4}$ of them were freshmen, $\frac{1}{3}$ were sophomores, and half of the remaining students were juniors. We need to find out how many seniors were in the survey.
Calculate Freshmen: Calculate the number of freshmen by taking $\frac{1}{4}$ of the total number of students. $\newline$ $(\frac{1}{4}) \times 336 = 84$ $\newline$ There were $84$ freshmen in the survey.
Calculate Sophomores: Calculate the number of sophomores by taking $\frac{1}{3}$ of the total number of students. $\newline$ $(\frac{1}{3}) \times 336 = 112$ $\newline$ There were $112$ sophomores in the survey.
Calculate Remaining Students: Subtract the number of freshmen and sophomores from the total number of students to find the number of remaining students. $\newline$ $336 - 84 - 112 = 140$ $\newline$ There are $140$ students remaining after accounting for freshmen and sophomores.
Calculate Juniors: Calculate the number of juniors by taking half of the remaining students. $\newline$ $140 / 2 = 70$ $\newline$ There were $70$ juniors in the survey.
Calculate Seniors: Subtract the number of juniors from the remaining students to find the number of seniors. $\newline$ $140 - 70 = 70$ $\newline$ There were $70$ seniors in the survey.