4. Tomi dropped a rubber ball from a certain height onto a hard floor. After each bounce, it reached $\frac{3}{4}$ of the previous height. The ball bounced four times from the ground. At the moment it fell for the fifth time, his neighbor Jani caught it. From what height did Tomi drop the ball if it traveled a total distance of $653 \mathrm{~cm}$? Write down your answer.
4. Let the height from which the ball is dropped to the ground be $x$. After the first bounce from the ground, the ball reached $\frac{3}{4} x$ of the initial height, just as much when dropped from that height. After the second bounce, the ball reached $\frac{3}{4}\left(\frac{3}{4} x\right)=\frac{9}{16} x$ of the initial height, just as much when dropped. After the third bounce and drop, the ball traveled a distance of $\frac{27}{64} x \cdot 2$. After the fourth bounce and drop, the ball traveled a distance of $\frac{81}{256} x \cdot 2$. Thus, the total distance traveled by the ball is $x+2 x\left(\frac{3}{4}+\frac{9}{16}+\frac{27}{64}+\frac{81}{256}\right)=653$. We rearrange the equation to $653=\frac{653}{128} x$ and solve for $x=128 \mathrm{~cm}$.

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