Double ratio

The mobile phone was twice gradually discounted in the ratio of 3: 2 1 half: 5 quarters. How much did it originally cost if the price was CZK 4,200 after a double discount?

Correct result:

a =  10080

Solution:

$$\begin{gathered} c=4200 \\ a:b:c=3:(2+1\mathrm{/}2):(5\mathrm{/}4) \\ b:c=(2+1\mathrm{/}2):(5\mathrm{/}4) \\ b=(2+1\mathrm{/}2)\mathrm{/}(5\mathrm{/}4)\cdot c=(2+1\mathrm{/}2)\mathrm{/}(5\mathrm{/}4)\cdot 4200=8400 \\ a:b=3:(2+1\mathrm{/}2) \\ a=3\mathrm{/}(2+1\mathrm{/}2)\cdot b=3\mathrm{/}(2+1\mathrm{/}2)\cdot 8400=10080 \\ \text{ Verifying Solution: } \\ {a}_1=3\mathrm{/}(5\mathrm{/}4)\cdot c=3\mathrm{/}(5\mathrm{/}4)\cdot 4200=10080 \end{gathered}$$

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