Ondra book pages

Andrew was reading a book. On the first day, he read one-tenth. On the second day, he read half of the remainder. On the third day, he read 20% of the new remainder, and on the fourth day, he read the remaining 72 pages. How many pages did the book have?

Final Answer:

a =  200

Step-by-step explanation:

$$\begin{gathered} d=72 \\ {r}_3=20\%=\frac{20}{100}=\frac{1}{5}=0.2 \\ c-r_3\cdot c=d \\ c-0.2\cdot c=72 \\ 0.8c=72 \\ c=\frac{72}{0.8}=90 \\ c=90 \\ b-b/2=c \\ b-b/2=90 \\ b=180 \\ a-a/10=b \\ a-a/10=180 \\ 9a=1800 \\ a=\frac{1800}{9}=200 \\ a=200 \\ \text{ Verifying Solution: } \\ B=a-a/10=200-200/10=180 \\ C=B-B/2=180-180/2=90 \\ D=C-0.20\cdot C=90-0.20\cdot 90=72 \\ E=D-D=72-72=0 \end{gathered}$$

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