Question

Оля читала повесть по 9 страниц в день, хотя, возможно, в последний день ей осталось прочесть меньше девяти страниц. Катя начала читать эту же повесть одновременно с Олей, но Катя читала по 10 страниц каждый день, хотя в последний день могло остаться меньше. Оля и Катя закончили читать повесть в один и тот же день, потратив на чтение не меньше девяти дней. Сколько страниц в повести?

Answer 1

1)9х9=81
2)10х9=90
3)1<10=10х9=81

Answer 2

Problem Analysis

We are given the information about two people, Olga (Olya) and Katya (Katy), who are reading a novel. Olga reads 9 pages per day, while Katya reads 10 pages per day. They both finish reading the novel on the same day, and it took them at least 9 days to finish. We need to determine the total number of pages in the novel.

Solution

Let's assume the total number of pages in the novel is P.

From the given information, we know that Olga reads 9 pages per day, and it took her at least 9 days to finish the novel. Therefore, the minimum number of pages Olga could have read is 9 * 9 = 81 pages.

Similarly, Katya reads 10 pages per day, and it took her at least 9 days to finish the novel. Therefore, the minimum number of pages Katya could have read is 10 * 9 = 90 pages.

Since both Olga and Katya finished reading the novel on the same day, the total number of pages in the novel must be a common multiple of the minimum number of pages they could have read.

To find the common multiple, we can find the least common multiple (LCM) of 81 and 90.

Finding the Least Common Multiple (LCM)

To find the LCM of two numbers, we can use the prime factorization method or the division method. Let's use the division method to find the LCM of 81 and 90.

1. Divide each number by its smallest prime factor: - 81 ÷ 3 = 27 - 90 ÷ 2 = 45

2. Divide the resulting numbers by their smallest prime factors: - 27 ÷ 3 = 9 - 45 ÷ 3 = 15

3. Divide the resulting numbers by their smallest prime factors: - 9 ÷ 3 = 3 - 15 ÷ 3 = 5

4. Divide the resulting numbers by their smallest prime factors: - 3 ÷ 3 = 1 - 5 ÷ 5 = 1

The prime factorization of 81 is 3^4, and the prime factorization of 90 is 2 * 3^2 * 5.

To find the LCM, we multiply the highest power of each prime factor: LCM = 2 * 3^4 * 5 = 2 * 81 * 5 = 810.

Therefore, the total number of pages in the novel is 810.

Answer

The novel has 810 pages.