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(50*r)/(50+r)=9,5 umstellen nach r

\(\small{ \begin{array}{rcl} \dfrac{ 50\cdot r} { 50+r } &=& 9,5 \\ \\ \dfrac{ 50\cdot r} { 50+r }\cdot \dfrac{(50\cdot r)}{(50\cdot r)} &=& 9,5 \\ \\ \dfrac{ \frac{50\cdot r}{50\cdot r} } { \frac{50}{50\cdot r} +\frac{r}{50\cdot r} } &=& 9,5 \\\\ \dfrac{ 1 } { \frac{1}{r} +\frac{1}{50} } &=& 9,5 \\\\ \dfrac{1}{r} +\dfrac{1}{50} &=& \dfrac{1}{9,5}\\\\ \dfrac{1}{r} &=& \dfrac{1}{9,5}-\dfrac{1}{50}\\\\ \dfrac{1}{r} &=& \dfrac{50-9,5}{50\cdot 9,5}\\\\ r &=& \dfrac{50\cdot 9,5}{50-9,5}\\\\ r &=& \dfrac{475}{40,5}\\\\ r &=& \dfrac{4750}{405}\\\\ r &=& \dfrac{950}{81}\\\\ r &=& 11\dfrac{59}{81}\\\\ \mathbf{r} &\mathbf{=} & \mathbf{11.7283950617} \end{array} }\)

Hallo anonymous!

(50 * r) / (50 + r) = 9,5     Umstellen nach r

(50 * r) / (50 + r) = 9,5                       [ * (50 + r)

50r = 9,5 * (50 + r)  

50r = 475 + 9,5r                               [ -  9,5r

40,5r = 475                                      [ / 40,5

r = 475 / 40,5 = 4750 / 405                [ erweitern mit 10, kürzen durch 5

r = 950 / 81

r = 11 + 59/81

Probe:

(50 * r) / (50 + r) = 9,5  

(50 * (11 + 59/81)) / (50 + 11 + 59/81) = 9,5

9,5 = 9,5                                            okay 

Gruß  asinus :- )