Factory and divisions

The factory consists of three auxiliary divisions total of 2,406 employees. The second division has 76 employees less than the 1st division, and the 3rd division has 212 employees more than the 2nd. How many employees have each division?

Correct answer:

a =  782
b =  706
c =  918

Step-by-step explanation:


a+b+c=2406
b = a - 76
c = b + 212

a+b+c = 2406
a-b = 76
b-c = -212

Row 2 - Row 1 → Row 2
a+b+c = 2406
-2b-c = -2330
b-c = -212

Row 3 - 1/-2 · Row 2 → Row 3
a+b+c = 2406
-2b-c = -2330
-1.5c = -1377


c = -1377/-1.5 = 918
b = -2330+c/-2 = -2330+918/-2 = 706
a = 2406-b-c = 2406-706-918 = 782

a = 782
b = 706
c = 918

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