Give the step-by-step reasoning process and then the final answer. In a school with 800 students, 5/8 of the students are girls. Seven-tenths of the girls and two-fifths of the boys are in the primary grades, while the rest are middle schoolers. How many middle schoolers are there?
There are 800 x 5 / 8 = 500 girls. So, there are 800 - 500 = 300 boys. There are 500 x 7 / 10 = 350 girls that are in the primary grades. Hence, 500 - 350 = 150 girls are middle schoolers. There are 300 x 2 / 5 = 120 boys that are in the primary grades. Hence, 300 - 120 = 180 boy students are middle schoolers. Therefore, a total of 150 girls + 180 boys = 330 middle schoolers.
The final answer: 330.