Before yesterday

He merchant adds a sale sign in his shop window to the showed pair of shoes in the morning: "Today by p% cheaper than yesterday. " After a while, however, he decided that the sign saying: "Today 62.5% cheaper than the day before yesterday". Determine the number p.

Result

p =  25 %

Solution:

x (12p/100) (1p/100)=x (162.5/100)  (12p/100) (1p/100)=162.5/100   (1002p) (100p)=100 (10062.5) 2p2300p+6250=0  a=2;b=300;c=6250 D=b24ac=3002426250=40000 D>0  p1,2=b±D2a=300±400004 p1,2=300±2004 p1,2=75±50 p1=125 p2=25   Factored form of the equation:  2(p125)(p25)=0 0<p<100  p=p2=25=25%x \cdot \ (1-2p/100) \cdot \ (1-p/100) = x \cdot \ (1 - 62.5/100) \ \\ \ \\ (1-2p/100) \cdot \ (1-p/100) = 1 - 62.5/100 \ \\ \ \\ \ \\ (100-2p) \cdot \ (100-p) = 100 \cdot \ (100 - 62.5) \ \\ 2p^2 -300p +6250 = 0 \ \\ \ \\ a = 2; b = -300; c = 6250 \ \\ D = b^2 - 4ac = 300^2 - 4\cdot 2 \cdot 6250 = 40000 \ \\ D>0 \ \\ \ \\ p_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 300 \pm \sqrt{ 40000 } }{ 4 } \ \\ p_{1,2} = \dfrac{ 300 \pm 200 }{ 4 } \ \\ p_{1,2} = 75 \pm 50 \ \\ p_{1} = 125 \ \\ p_{2} = 25 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 2 (p -125) (p -25) = 0 \ \\ 0<p<100 \ \\ \ \\ p = p_{ 2 } = 25 = 25 \%

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