Question

Как решить? В городе 1022 автобуса тролейбус и трамвай.Автобус в 4.5 раза больше чем трамваев а тродейбусов на 258 меньше чем автобусов.Сколько в городе автобусов? тролейбусов?

Answer 1

Автобусів-576
Тролейбусів-318
Трамваїв-128
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Answer 2

Problem Analysis

To solve this problem, we need to determine the number of buses and trolleybuses in the city based on the given information. We are told that there are 1022 buses, trolleybuses, and trams combined. Additionally, we are given the following information: - The number of buses is 4.5 times greater than the number of trams. - The number of trolleybuses is 258 less than the number of buses.

Solution

Let's assume the number of trams in the city is x. Based on the given information, we can derive the following equations:

1. The number of buses is 4.5 times greater than the number of trams: - Number of buses = 4.5 * Number of trams = 4.5x

2. The number of trolleybuses is 258 less than the number of buses: - Number of trolleybuses = Number of buses - 258 = 4.5x - 258

We know that the total number of buses, trolleybuses, and trams combined is 1022. Therefore, we can write the equation:

3. Number of buses + Number of trolleybuses + Number of trams = 1022

Now, let's substitute the expressions for the number of buses and trolleybuses from equations 1 and 2 into equation 3:

4. 4.5x + (4.5x - 258) + x = 1022

Simplifying equation 4:

5. 10x - 258 = 1022

Adding 258 to both sides:

6. 10x = 1280

Dividing both sides by 10:

7. x = 128

Therefore, the number of trams in the city is 128.

To find the number of buses, we can substitute the value of x into equation 1:

Number of buses = 4.5 * 128 = 576

To find the number of trolleybuses, we can substitute the value of x into equation 2:

Number of trolleybuses = 4.5 * 128 - 258 = 330

Answer

Based on the given information, there are 576 buses and 330 trolleybuses in the city.