Sale discount

The product was discounted so that eight products at a new price cost just as five products at an old price. How many percents is the new price lower than the old price?

Correct answer:

p =  37.5 %

Step-by-step explanation:

$$\begin{gathered} 8y=5x \\ y=(1-p\mathrm{/}100)x \\ 8(1-p\mathrm{/}100)x=5x \\ 8(1-p\mathrm{/}100)=5 \\ 8\cdot (1-p\mathrm{/}100)=5 \\ 8p=300 \\ p={\displaystyle \frac{75}{2}}=37.5=37.5\mathrm{\%} \end{gathered}$$

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