Question

ПОМОГИТЕ!!!!!!!!!!!!!!!!!!!!!Первая машинистка, работая одна, перепечатывает рукопись объёмом 240 страниц за 7 дней, а вторая эту же рукопись перепечатывает за 5 дней. Рукопись разделили между ними таким образом, чтобы они закончили работу одновременно. Сколько получила страниц первая машинистка?РЕШЕНИЕ ПОЖАЛУЙСТА. ВАРИАНТЫ ОТВЕТА:А) 100 СТРАНИЦ; Б) 140 СТРАНИЦ; В) 160 СТРАНИЦ.с пояснением и еще оответ должен получится 100 но как это показать?

Answer 1

Пусть первой машинистке дали х листов, тогда второй - (240-х).
Скорость первой машинистки 240/7, значит она на работу потратит х:(240/7) дней.
Скорость второй - 240/5 и на работу она потратит (240-х):(240/5) дней.
Так как работа будет закончена одновременно, то получаем уравнение:
$\frac{x}{ \frac{240}{7} }= \frac{240-x}{ \frac{240}{5} }$
$\frac{7x}{240}= \frac{5(240-x)}{240}$
7x=5(240-x)
7x=1200-5x
12x=1200
x=100

Answer 2

Problem Analysis

We are given that the first typist can transcribe a manuscript of 240 pages in 7 days, while the second typist can transcribe the same manuscript in 5 days. We need to determine how many pages the first typist transcribed.

Solution

Let's assume that the first typist transcribed x pages of the manuscript. Since the first typist can transcribe the entire manuscript in 7 days, their daily transcription rate would be x/7 pages per day. Similarly, the second typist's daily transcription rate would be x/5 pages per day.

Since both typists are working simultaneously and we want them to finish at the same time, their combined daily transcription rate should be equal to the total number of pages in the manuscript divided by the total number of days it takes for them to finish.

The total number of pages in the manuscript is given as 240, and the total number of days it takes for them to finish is the least common multiple (LCM) of 7 and 5, which is 35.

Using the above information, we can set up the following equation:

x/7 + x/5 = 240/35

To solve this equation, we can multiply both sides by the least common multiple of 7 and 5, which is 35:

5x + 7x = 240 * 35

Simplifying the equation:

12x = 240 * 35

x = (240 * 35) / 12

Evaluating the expression:

x = 700

Therefore, the first typist transcribed 700 pages of the manuscript.

Answer

The first typist transcribed 700 pages of the manuscript.

Note: The answer is not one of the options provided (100, 140, or 160 pages).