# Three piles

100 kg of sugar we divide into three piles. The first pile is small. If we added to the second 2 kg of sugar, it would have 25% more sugar than the first pile. If we add 3 kg of sugar to the third pile, it would have 20% more sugar than the 2nd pile. How many kilograms of sugar are on each pile?

a =  28.64
b =  33.8
c =  37.56

## Step-by-step explanation:

a+b+c=100
b+2 = 1.25 a
c+3 = 1.20 b

a+b+c=100
b+2 = 1.25·a
c+3 = 1.20·b

a+b+c = 100
1.25a-b = 2
1.2b-c = 3

Pivot: Row 1 ↔ Row 2
1.25a-b = 2
a+b+c = 100
1.2b-c = 3

Row 2 - 1/1.25 · Row 1 → Row 2
1.25a-b = 2
1.8b+c = 98.4
1.2b-c = 3

Row 3 - 1.2/1.8 · Row 2 → Row 3
1.25a-b = 2
1.8b+c = 98.4
-1.667c = -62.6

c = -62.6/-1.66666667 = 37.56
b = 98.4-c/1.8 = 98.4-37.56/1.8 = 33.8
a = 2+b/1.25 = 2+33.8/1.25 = 28.64

a = 716/25 = 28.64
b = 169/5 = 33.8
c = 939/25 = 37.56

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