Concert Ticket Prices

A total of 256 tickets were sold for the concert. CZK 2,800 was collected for tickets under the stage, and CZK 2,160 for tickets to the corridors. Determine the price of tickets under the stage and on the corridors, if you know that the ticket under the podium was CZK 10 more expensive than the ticket on the corridor.

Final Answer:

a =  25 kc
b =  15 kc

Step-by-step explanation:

$$\begin{gathered} a=10+b \\ 2800/a+2160/b=256 \\ 2800b+2160a=256ab \\ 2800(a-10)+2160a=256a(a-10) \\ -256a^2+7520a-28000=0 \\ 256a^2-7520a+28000=0 \\ 256=2^8 \\ 7520=2^5\cdot 5\cdot 47 \\ 28000=2^5\cdot 5^3\cdot 7 \\ \text{GCD}(256,7520,28000)=2^5=32 \\ 8a^2-235a+875=0 \\ p=8;q=-235;r=875 \\ D=q^2-4pr=235^2-4\cdot 8\cdot 875=27225 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{235\pm \sqrt{27225}}{16} \\ {a}_{1,2}=\frac{235\pm 165}{16} \\ {a}_{1,2}=14.6875\pm 10.3125 \\ {a}_1=25 \\ {a}_2=4.375 \\ a=a_1=25=25\text{kc} \end{gathered}$$

Our quadratic equation calculator calculates it.

$b=a-10=25-10=15\text{kc}$

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