Individual

On the hill behind Terchová, there is a sheepfold and a shepherd lives in it. He divided two hundred of his sheep into 4 groups in a mysterious way:
If he had 4 more sheep in the first group, 4 fewer in the second, 4 times more in the third, and 4 times less in the fourth, he would also have sheep in each group.

Find out how big the individual groups are.

Correct answer:

a =  28
b =  36
c =  8
d =  128

Step-by-step explanation:


a+b+c+d = 200
a+4 = b-4
b-4 = 4c
4c = d/4

a+b+c+d = 200
a+4 = b-4
b-4 = 4·c
4·c = d/4

a+b+c+d = 200
a-b = -8
b-4c = 4
16c-d = 0

Row 2 - Row 1 → Row 2
a+b+c+d = 200
-2b-c-d = -208
b-4c = 4
16c-d = 0

Row 3 - 1/-2 · Row 2 → Row 3
a+b+c+d = 200
-2b-c-d = -208
-4.5c-0.5d = -100
16c-d = 0

Pivot: Row 3 ↔ Row 4
a+b+c+d = 200
-2b-c-d = -208
16c-d = 0
-4.5c-0.5d = -100

Row 4 - -4.5/16 · Row 3 → Row 4
a+b+c+d = 200
-2b-c-d = -208
16c-d = 0
-0.7813d = -100


d = -100/-0.78125 = 128
c = 0+d/16 = 0+128/16 = 8
b = -208+c+d/-2 = -208+8+128/-2 = 36
a = 200-b-c-d = 200-36-8-128 = 28

a = 28
b = 36
c = 8
d = 128

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