one-half of the students in a city school plan to enter liberal arts colleges and one-third of the students plan to go to junior college.The remaining 300 pupils expect to seek permanent employment after graduation.How many students are there in this school?

0.5x + 0.333x + 300 = x

Solve for x.

1800

To find the total number of students in the school, we need to add the number of students planning to enter liberal arts colleges, the number of students planning to go to junior college, and the number of students expecting to seek permanent employment after graduation.

Let's start with the students planning to enter liberal arts colleges. We are given that one-half of the students plan to do so. So, if we let "x" represent the total number of students, we can say that:

Number of students planning to enter liberal arts colleges = 1/2 * x

Next, we have the students planning to go to junior college. We are given that one-third of the students plan to do so. So, the number of students planning to go to junior college is:

Number of students planning to go to junior college = 1/3 * x

Finally, we have the number of students expecting to seek permanent employment after graduation, which is already given as 300.

Now, we can add these three quantities together to find the total number of students:

1/2 * x + 1/3 * x + 300 = x

To simplify the equation, we can multiply all terms by the least common multiple of 2 and 3, which is 6:

6 * (1/2 * x) + 6 * (1/3 * x) + 6 * 300 = 6 * x

3x + 2x + 1800 = 6x

5x + 1800 = 6x

Subtract 5x from both sides:

1800 = 6x - 5x

1800 = x

Therefore, the total number of students in the school is 1800.