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:

c=4200 a:b:c=3:(2+1/2):(5/4)  b:c=(2+1/2):(5/4)  b=(2+1/2)/(5/4)⋅ c=(2+1/2)/(5/4)⋅ 4200=8400  a:b=3:(2+1/2) a=3/(2+1/2)⋅ b=3/(2+1/2)⋅ 8400=10080   Verifying Solution:  a1=3/(5/4)⋅ c=3/(5/4)⋅ 4200=10080

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