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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 :

SlowZasob
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.
fichoh

The total number of students in the entire school when all students are present is 200 students.

Let the number of students in each class = n

We could set up an equation relating to the given scenario thus :

5(1/2n) + 3(3/4n) + 2(n - 1/8) = 10n - 70

5n/2 + 9n/4 + 2(7n/8) = 10n - 70

5n/2 + 9n/4 + 14n/8 = 10n - 70

L.C.M of 2, 4 and 8 = 8

(20n + 18n + 14n) /8 = (10n - 70)

Cross multiply :

52n = 8(10n - 70)

52n = 80n - 560

Subtract 80n from both sides:

52n - 80n = - 560

-28n = - 560

n = 560/28

n = 20

Hence, Number of students in each class = 20

Therefore, the total number of students in the entire school is 10n = 10 × 20 = 200 students

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