# Construction 2449

The construction material was taken away by three different large cars. The weight of the load on the second was 20% more than on the first. The weight on the third was 20% more than on the second. They loaded a total of 18.2 tons. How many tons were on each car?

a =  5 t
b =  6 t
c =  7.2 t

## Step-by-step explanation:

b = 1.2 a
c = 1.2 b
a+b+c = 18.2

b = 1.2·a
c = 1.2·b
a+b+c = 18.2

1.2a-b = 0
1.2b-c = 0
a+b+c = 18.2

Row 3 - 1/1.2 · Row 1 → Row 3
1.2a-b = 0
1.2b-c = 0
1.833b+c = 18.2

Pivot: Row 2 ↔ Row 3
1.2a-b = 0
1.833b+c = 18.2
1.2b-c = 0

Row 3 - 1.2/1.83333333 · Row 2 → Row 3
1.2a-b = 0
1.833b+c = 18.2
-1.655c = -11.913

c = -11.91272727/-1.65454545 = 7.2
b = 18.2-c/1.83333333 = 18.2-7.2/1.83333333 = 6
a = 0+b/1.2 = 0+6/1.2 = 5

a = 5
b = 6
c = 36/5 = 7.2

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