Class pupil distribution

There are a total of 56 pupils in three classes in the rural school. In the second grade, there are 20% fewer pupils than in the first grade, and in the third grade, there are 25% more pupils than in the second grade. How many pupils are there in each class?

Final Answer:

a =  20
b =  16
c =  20

Step-by-step explanation:


a+b+c=56
b = a - 0.20a
c = b+0.25b

a+b+c=56
b = a - 0.20·a
c = b+0.25·b

a+b+c = 56
0.8a-b = 0
1.25b-c = 0

Row 2 - 0.8 · Row 1 → Row 2
a+b+c = 56
-1.8b-0.8c = -44.8
1.25b-c = 0

Row 3 - 1.25/-1.8 · Row 2 → Row 3
a+b+c = 56
-1.8b-0.8c = -44.8
-1.556c = -31.111


c = -31.11111111/-1.55555556 = 20
b = -44.8+0.8c/-1.8 = -44.8+0.8 · 20/-1.8 = 16
a = 56-b-c = 56-16-20 = 20

a = 20
b = 16
c = 20

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