Question

Автобус за 12 рейсов перевёз больше 235 пассажиров, а за 20 рейсов — меньше 405 пассажиров. Определить число мест в автобусе, если в каждом рейсе число пассажиров было равно числу мест в автобусе

Answer 1

12x>235 20x<405 x>235:12 x<405:20 x>19,5 x<20,2 ответ:20 мест

Answer 2

Problem Analysis

We are given that a bus carried more than 235 passengers in 12 trips and fewer than 405 passengers in 20 trips. We need to determine the number of seats on the bus, assuming that the number of passengers in each trip was equal to the number of seats on the bus.

Solution

Let's solve this problem step by step.

1. We know that the bus carried more than 235 passengers in 12 trips. This means that the total number of passengers in these 12 trips is greater than 235. Let's denote the number of seats on the bus as x. Therefore, the total number of passengers in these 12 trips is 12x.

2. We also know that the bus carried fewer than 405 passengers in 20 trips. This means that the total number of passengers in these 20 trips is less than 405. Therefore, the total number of passengers in these 20 trips is 20x.

3. From the given information, we can write two inequalities: - 12x > 235 (The total number of passengers in 12 trips is greater than 235) - 20x < 405 (The total number of passengers in 20 trips is less than 405)

4. Let's solve these inequalities to find the range of possible values for x.

- Solving the first inequality: ``` 12x > 235 x > 235/12 x > 19.58 ``` Therefore, x must be greater than 19.58.

- Solving the second inequality: ``` 20x < 405 x < 405/20 x < 20.25 ``` Therefore, x must be less than 20.25.

5. Combining the results from step 4, we can conclude that the number of seats on the bus (x) must be an integer greater than 19.58 and less than 20.25.

6. Since the number of seats on a bus cannot be a fraction or a decimal, we can round up the lower limit and round down the upper limit to the nearest integer.

- Rounding up the lower limit: x > 19.58 → x ≥ 20 - Rounding down the upper limit: x < 20.25 → x ≤ 20

7. Therefore, the number of seats on the bus must be 20.

Answer

The number of seats on the bus is 20.