# The library

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

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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