Trousers

Jarek bought new trousers, but the trousers were too long. Their length was in the ratio of 5:8 to Jarek's height. The mother cut his trousers by 4 cm. Thus, the original ratio decreased by 4%.

Determine Jarek's high.

Final Answer:

v =  160 cm

Step-by-step explanation:

$$\begin{gathered} n:v=5:8=5/8 \\ 8n=5v \\ q=100\%-4\%=1-\frac{4}{100}=0.96 \\ n-4=5/8\cdot v\cdot q \\ 5/8v-4=5/8\cdot v\cdot q \\ 5/8v-4=5/8\cdot v\cdot 0.96 \\ 5/8\cdot v-4=5/8\cdot v\cdot 0.96 \\ 0.2v=32 \\ v=\frac{32}{0.2}=160 \\ v=160=160\text{cm} \end{gathered}$$

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