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。
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.
Little Ming read a book. He read 15 pages in the first 4 days and 6 pages a day in the next 5 days. How many pages did he read on average every day?
Xiao Ming read a book for the first 4 days and read 15 pages, then read 6 pages every day for 5 days. We can use the following formula to calculate the average number of pages seen per day: Average number of pages read per day = total number of pages/days Substituting the total number of pages and the number of days into the formula, we get: Average number of pages read per day = 15 pages/4 days = 3 pages/day Therefore, Xiao Ming read an average of three pages a day.
Xiao Ming read a book. He read 72 pages in the first 4 days and 29 pages a day for the next 6 days. How many pages did he read on average every day?
If Xiaoming reads 72 pages in the first 4 days, then Xiaoming's total page count in the first 4 days is 72 pages. Reading 29 pages every day for the next 6 days would mean that the total number of pages for the next 6 days would be 29 pages x 6 days = 171 pages. Therefore, Little Ming's total page count in the last six days was 171 pages. Little Ming read 171 pages per day for the next 6 days, 6 days = 27 pages. Therefore, Xiao Ming read an average of 27 pages a day.
Little Ming read a book and read 120 of the book every day. After 5 days, there were 120 pages left. How many pages does this book have? He still needs a few days to finish reading it)
This book had a total of $1/20/div1/20 = 600$pages. Little Ming still needed $5/div2 = 2$days to finish reading this book.
Chen Ming read a storybook and read an average of 11 pages a day for the first three days. He read an average of 18 pages a day for the next four days. How many pages did Chen Ming read on average in the past seven days?
Suppose the book has a total of x pages, and Chen Ming has read a total of y pages in these seven days: - Chen Ming read 11*3=33 pages in the first three days - In the next three days, Chen Ming read a total of 18*3=54 pages - In seven days, Chen Ming read a total of y*7=497 pages Therefore, Chen Ming read an average of 497/7=74 pages a day in the past seven days.
A book had a total of 260 pages, and Xiao Ming had already read 80 pages. He had to finish the rest in five days. How many pages did he read on average every day?
Xiao Ming needed to finish reading the remaining 260 pages in 5 days, so he needed to read 260 pages per day divided by 5 days = 52 pages.
Xiao Jun read a book and read two-thirds of the book in seven days. In the next five days, he read a total of 40 pages and just finished it. How many pages are there in this book?
Suppose the book has x pages: Seven days ago, Xiao Jun read 7 × 2/3 = 14/3 pages, which was 14/3 div7 = 4/9 pages. Xiao Jun read (x + 5) × 4/5 = x + 20/3 pages in the last 5 days. Because Xiao Jun had read a total of 40 pages, there were: 4/9 + 20/3 = x The solution was x = 360/9 + 20/3 = 480/3 pages. Therefore, this book had a total of 480/3 pages.
Wang Qiang read a book. For the first four days, he read eight pages a day, and for the next three days, he read a total of 17 pages. How many pages did he read on average every day?
Wang Qiang read a book for the first four days, eight pages a day, and then a total of 17 pages for the next three days. We can split this situation into two parts for analysis: Reading eight pages a day for the first four days meant that Wang Qiang had already read $4/times 8 = 32$pages in the first four days. Reading a total of 17 pages in the last 3 days meant that Wang Qiang had read another $3/17 = 54$page in the last 3 days. Therefore, Wang Qiang read a total of $32+54=86$pages. Next, we need to calculate how many pages he reads on average every day. Did he read all the books in the first four days and the last three days together? If that was the case, then the average number of pages he read every day was $86/4+17/3=265+5=315$pages. If not, then the average number of pages he read every day was $86/4-17/3=26-5=21$pages. Therefore, Wang Qiang read an average of 21 pages a day.
A book has 36 pages. Xiao Ming finished reading it in 9 days. On average, how much does he read every day?
A book has 36 pages. Xiaoming needs 9 days to finish reading it. So, the average number of pages that Xiaoming reads every day is: 36 pages/9 days = 34 pages/day Therefore, Xiao Ming read an average of 34 pages of this book every day.
Xiao Lin spent five days to finish reading a 70-page book. On average, how much of the book did he read every day? How much of this book did he read in three days?
Kobayashi spent five days to finish reading a 70-page book. On average, he would read the book every day (page count/days)×(days/2)= (70/5)×(5/2)=14 pages/day. 3 days to read this book (page count/day count)×(day count/2)= (70/3)×(3/2)=20 pages/day.