Car loads

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?

Final Answer:

a =  5 t
b =  6 t
c =  7.2 t

Step-by-step explanation:

$$\begin{gathered} r=100\%+20\%=1+\frac{20}{100}=1.2 \\ b=ra \\ c=rb \\ a+b+c=18.2 \\ a+r\cdot a+r\cdot b=18.2 \\ a+r\cdot a+r\cdot r\cdot a=18.2 \\ a+1.2\cdot a+1.2\cdot 1.2\cdot a=18.2 \\ 3.64a=18.2 \\ a=\frac{18.2}{3.64}=5 \\ a=5=5\text{t} \end{gathered}$$

$b=r\cdot a=1.2\cdot 5=6\text{t}$

$c=r\cdot b=1.2\cdot 6=7.2\text{t}$

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