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?

Result

a =  10080

Solution:

$c=4200 \ \\ a:b:c=3:(2 + 1/2):(5/4) \ \\ \ \\ b:c=(2 + 1/2):(5/4) \ \\ \ \\ b=(2 + 1/2)/(5/4) \cdot \ c=(2 + 1/2)/(5/4) \cdot \ 4200=8400 \ \\ \ \\ a:b=3:(2 + 1/2) \ \\ a=3/(2+1/2) \cdot \ b=3/(2+1/2) \cdot \ 8400=10080 \ \\ \ \\ \text{ Correctness test: } \ \\ a_{1}=3/(5/4) \cdot \ c=3/(5/4) \cdot \ 4200=10080$

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