The library

Anna stored a total of 126 books in three compartments of a library. The first compartment has 6 more books than the second. The number of books in the second compartment is the arithmetic mean of the number in the first and third compartments. Calculate how many books are in each compartment.

Final Answer:

a =  48
b =  42
c =  36

Step-by-step explanation:


a+b+c=126
a = 6+b
b = (a+c)/2

a+b+c = 126
a-b = 6
a-2b+c = 0

Row 2 - Row 1 → Row 2
a+b+c = 126
-2b-c = -120
a-2b+c = 0

Row 3 - Row 1 → Row 3
a+b+c = 126
-2b-c = -120
-3b = -126

Pivot: Row 2 ↔ Row 3
a+b+c = 126
-3b = -126
-2b-c = -120

Row 3 - -2/-3 · Row 2 → Row 3
a+b+c = 126
-3b = -126
-c = -36


c = -36/-1 = 36
b = -126/-3 = 42
a = 126-b-c = 126-42-36 = 48

a = 48
b = 42
c = 36

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