Washing powder

A 10-kilogram pack of washing powder is M euros more expensive than a 5-kilogram pack of the same powder. A 5-kilogram package costs P euros. Five kilos of packaging is not worth it because it is more expensive than half the price of 10 kilos. How much is 1 kg of a 10-kilogram pack cheaper than 1 kg of a 5-kilogram pack? Express the result using the parameters M and P.

Correct answer:

p = % 50 * (P-M)/P

Step-by-step explanation:

$$\begin{gathered} m_5=P \\ {m}_{10}=M+m_5=M+P \\ {m}_5>m_{10}/2 \\ p=100\cdot \frac{m_5/5-m_{10}/10}{m_5/5} \\ p=100\cdot \frac{m_5-m_{10}/2}{m_5} \\ p=100\cdot \frac{P-(M+P)/2}{P} \\ p=100\cdot \frac{2P-M-P}{2P} \\ p=100\cdot \frac{P-M}{2P} \\ p=50\cdot \frac{P-M}{P} \\ p=50\cdot (P-M)/P \end{gathered}$$

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