Collected 61474

Three students collected a total of 32 kg of paper. The second student collected three times more paper than the first student, and the third student collected 2 kg more than the first student. How many kilograms of paper did each of them collect?

Correct answer:

a =  6
b =  18
c =  8

Step-by-step explanation:


a+b+c=32
b=3·a
c = 2+a

a+b+c = 32
3a-b = 0
a-c = -2

Pivot: Row 1 ↔ Row 2
3a-b = 0
a+b+c = 32
a-c = -2

Row 2 - 1/3 · Row 1 → Row 2
3a-b = 0
1.333b+c = 32
a-c = -2

Row 3 - 1/3 · Row 1 → Row 3
3a-b = 0
1.333b+c = 32
0.333b-c = -2

Row 3 - 0.33333333/1.33333333 · Row 2 → Row 3
3a-b = 0
1.333b+c = 32
-1.25c = -10


c = -10/-1.25 = 8
b = 32-c/1.33333333 = 32-8/1.33333333 = 18
a = 0+b/3 = 0+18/3 = 6

a = 6
b = 18
c = 8

Our linear equations calculator calculates it.



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