Question

A school has 10 classes with the same number of students in each class. One day, the weather was bad and many students were absent. 5 classes were half full, 3 classes were 3/4 full and 2 classes were 1/8 empty. A total of 70 students were absent. How many students are in this school when no students are absent? 

Answer 1

Five half-full classes + three 3/4 full classes + 2 1/8 empty (which is 7/8 full) classes altogether give us 10 classes without 70 students. Let's assume that one class is x, so we can write it as:

5 * 1/2x + 3 * 3/4x + 2 * 7/8x = 10x - 70

After multiplying and changing it to decimals:

2,5x + 2,25x + 1,75x = 10x - 70
6,5x = 10x - 70     / - 6,5x (both sides)
0 = 3,5x - 70     / + 70 (both sides)
70 = 3,5x     / :3,5 (both sides)
x = 20

Check:

5 * 1/2 * 20 + 3 * 3/4 * 20 + 2 * 7/8 * 20 = 10 * 20 - 70
5 * 10 + 3 * 15 + 2 * 17,5 = 200 - 70
50 + 45 + 35 = 130
130 = 130

Correct - there are 20 students in each class (200 students overall)

Answer: There are 200 students in the school when no students are absent.