Transported 80813

Three Tatras transported 22.2 tons of sand. The second Tatra transported 20% more than the first, and the third Tatra 25% more than the second. How much did each Tatra take?

Correct answer:

a =  6 t
b =  7.2 t
c =  9 t

Step-by-step explanation:

$$\begin{gathered} r=100\%+20\%=1+\frac{20}{100}=1.2 \\ k=100\%+25\%=1+\frac{25}{100}=1.25 \\ m=22.2\text{t} \\ a+b+c=m \\ b=r\cdot a \\ c=k\cdot b \\ a+r\cdot a+k\cdot r\cdot a=m \\ a+1.2\cdot a+1.25\cdot 1.2\cdot a=22.2 \\ 3.7a=22.2 \\ a=\frac{22.2}{3.7}=6 \\ a=6=6\text{t} \end{gathered}$$

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

$c=k\cdot b=1.25\cdot 7.2=9\text{t}$

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