The same book

Alexander and Blanka bought the same book that had 240 pages. Blanka read four pages more a day than Alexander. Blanka read it before Alexander. Alexander read the book both weekend days longer. Using an equation or system of equations, calculate how many pages of the book Alexander read each day.

Correct answer:

a =  20

Step-by-step explanation:

$$\begin{gathered} b=a+4 \\ \frac{240}{a}-2=\frac{240}{a+4} \\ 240\cdot (a+4)-2\cdot a\cdot (a+4)=240\cdot a \\ 240\cdot (a+4)-2\cdot a\cdot (a+4)=240\cdot a \\ -2a^2-8a+960=0 \\ 2a^2+8a-960=0 \\ 2...\text{ prime number} \\ 8=2^3 \\ 960=2^6\cdot 3\cdot 5 \\ \text{GCD}(2,8,960)=2 \\ {a}^2+4a-480=0 \\ p=1;q=4;r=-480 \\ D=q^2-4pr=4^2-4\cdot 1\cdot (-480)=1936 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{-4\pm \sqrt{1936}}{2} \\ {a}_{1,2}=\frac{-4\pm 44}{2} \\ {a}_{1,2}=-2\pm 22 \\ {a}_1=20 \\ {a}_2=-24 \\ a>0 \\ a=a_1=20 \\ b=a+4=20+4=24 \end{gathered}$$

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