Little Ming read a book. After seven days, there was still a quarter of the book left. In the next five days, he read a total of 120 pages, just enough to finish it. How much did Little Ming read on average every day?
假设这本书有 $n$ 页小明读了 $x$ 天. 根据题意小明读了 $x$ 天后这本书还剩下 $1/4$ 于全书的比例即 $\frac{1}{4}n = \frac{1}{4}x(n-x)$. 接下来小明读了 $x+7$ 天后这本书还剩下 $1/4$ 于全书的比例即 $\frac{1}{4}x(n-x) + \frac{1}{4}x^2 + \frac{1}{4}x^3 + \frac{1}{4}x^4 + \frac{1}{4}x^5 = \frac{1}{4}n$. 化简得到 $x^5 - 4x^4 + 3x^3 - 12x^2 + 25x - 4n = 0$. 这是一个由 $5$ 个方程组成的线性方程组可以通过特征值或特征方程的方法求解. 特征值计算如下: 设 $a_1 = 1$$a_2 = -2$$a_3 = -3$$a_4 = -5$$a_5 = -1$则特征方程为 $a_1^5 + a_2^4 + a_3^3 + a_4^2 + a_5^1 = 0$. 解得 $a_1 = 1$$a_2 = -2$$a_3 = -3$$a_4 = -5$$a_5 = -1$因此 $x = (-2 + 3i)(-3 + 5i)(-5 + 1i) = 3$即小明读了 $3$ 天. 因此小明读这本书平均每天读 $3$ 页.
Little Red read a book and read 15 pages a day. After four days, she still had 3/5 of the book left. How many pages was this book?
Little Red reads a book 15 pages a day, and after 4 days, there is still 3/5 of the book left. We can assume that this book has x pages. According to the question, Little Red had read a total of $4/times 15 = 60$pages in 4 days. The remaining pages are 3/5 of the book, so there are: $$ 60\div 3/5=24 $$ Therefore, the book had 24 pages.
Little Red read a book and read 15 pages a day. After four days, she still had 3/5 of the book left. How many pages was this book?
Assuming that the book has a total of $x$pages, then Little Red has read $x/times 15$pages in 4 days. The remaining pages are 3/5 of the book's worth, so there are: $$x <times 15><times 3/5>= Total pages $$ Solve this equation: $$x = \frac{total pages}{15} = \frac{1200}{15} = 80$$ Therefore, the book had a total of 80 pages.
Zhang Ming read a book called "Simultaneously Composing". He read 30 pages a day. After 3 days, he still had 5/8 of the book left.
This book was a novel called "Simultaneously Written Essay". Reading 30 pages a day for 3 days and still not reading 5/8 of the book, you can come to the following conclusion: This book has 300 pages. Zhang Ming read 30 pages a day, so the number of pages he read a day accounted for 30/300=1/10. 3. He had not read the remaining 5/8 of the book, which meant that he still had 5/8 of the book left. The total number of pages he needed to read every day to finish this book was 300/(1+5/8)=160 pages. Therefore, Zhang Ming needed to read 160 pages a day to finish the book.
Xiao Ming read a book and read 15 pages a day. After reading for 4 days, he still had 2/5 of the book left. How many pages does this book have?
Xiao Ming read a total of $4/15 = 60$pages in 4 days. The remaining pages are $2/5$of the book, so the book has a total of $2/5/60 = 48$. Thus, the book had a total of 48 pages.
Xiao Ming reads a book, reads 15 pages a day, and after 4 days, there are still 3/5 of the book left unread. How many pages is this book?
Assuming that this book has $n$pages, Xiaoming reads $x$pages every day: $$ 4\times 15 = 3/5 \times n $$ The solution is $n = 50$. So this book has 50 pages.
If you read a book, you can read a quarter of the book on the first day, and two-fifths of the book on the second day. There are still 14 pages left. How many pages are there in this book?
Xiao Ming reads a book, and after 7 days, there is still 1/3 of the book left. In the next five days, he would read 60 pages in total. How many pages did Xiao Ming read on average every day?
After reading a book for 7 days, Xiao Ming still had 1/3 of the book left. This meant that he had read 1/3 of the book and the remaining 2/3 of the book needed to read 2/3 × 7 = 4/3 days. Reading a total of 60 pages in the next 5 days meant that Xiaoming had read (60/5) = 12 pages in these 5 days. Therefore, Xiaoming read an average of 12 pages a day.
Xiao Ming reads a book, reads 16 pages a day, and after 5 days, there are still 3/5 of the book left unread. How many pages does this book have?
Assuming the book has $x$pages: - Xiao Ming read $5$days and read $16$pages every day, so he read $5/times 16 = 80$pages. - The remaining pages are 3/5 of the book's worth, so there are: $$ x - 5 \times 16 = 3/5 \times x $$ The above formula was simplified to: $$ x = 320 $$ So this book is $320$pages.
Xiao Xiao read a book. She read 20 pages a day. After 5 days, she still had 60% of the book left. How many pages is this book?
Assuming that this book has $n$pages and Xiaoxiao reads $20$pages a day, then she reads a total of $/frac{20/times 5}=50$pages. The rest of the books have a total of $n-50$pages, where $/frac{60}{n}$represents the proportion of the number of pages in the book. If the ratio is simplified to $\frac{60}{n}=\frac{n-50}{n}\times 100$, then $n=1200$. So this book is $1200$pages.
Little Ming read a book and read 15 pages a day. After four days, there were still three-fifths of the book that he had not read. How many pages did this book have?
Xiao Ming reads a book every day, reads 15 pages, and after 4 days, there are still 3/5 of the book left. How many pages does this book have? Assuming that the book has a total of $x$pages, then the number of pages that Xiao Ming reads in 4 days is $15,4 = 60$pages. The remaining pages are 3/5 of the book's worth, so there are: $$ 60 \div (3/5) = 12 $$ So the book has a total of $12$pages.