Kohlrabies

The price of one kohlrabi increased by € 0.40. The number of kohlrabies that a customer can buy for € 4 has thus decreased by 5. Find out the new price of one kohlrabi in euros.

Correct result:

c =  0.8 Eur

Solution:

$$\begin{gathered} c=0.4+a \\ 4\mathrm{/}a=4\mathrm{/}c+5 \\ 4\mathrm{/}(c-0.4)=4\mathrm{/}c+5 \\ 4\ast c=4\ast (c-0.4)+5\ast c\ast (c-0.4) \\ 4\cdot c=4\cdot (c-0.4)+5\cdot c\cdot (c-0.4) \\ -5c^2+2c+1.6=0 \\ 5c^2-2c-1.6=0 \\ p=5;q=-2;r=-1.6 \\ D=q^2-4pr=2^2-4\cdot 5\cdot (-1.6)=36 \\ D>0 \\ {c}_{1,2}={\displaystyle \frac{-q\pm \sqrt{D}}{2p}}={\displaystyle \frac{2\pm \sqrt{36}}{10}} \\ {c}_{1,2}={\displaystyle \frac{2\pm 6}{10}} \\ {c}_{1,2}=0.2\pm 0.6 \\ {c}_1=0.8 \\ {c}_2=-0.4 \\ \text{ Factored form of the equation: } \\ 5(c-0.8)(c+0.4)=0 \\ c=c_1=0.8={\displaystyle \frac{4}{5}}={\displaystyle \frac{4}{5}}\text{ Eur}=0.8\text{ Eur} \end{gathered}$$

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