Question

для отправки детей в летний лагерь было подано 8 одинаковых автобусов. если бы в каждом автобусе было на 15 мест больше,то в них смогли бы разместиться 360 человек. сколько мест было в каждом из автобусов? постарайтесь решить задачу двумя способами: арифметически и алгебраически!

Answer 1

1 способ арифметический:

1)15*8=120 сколько мест всего добавили 

2)360-120=240 сколько поместилось первоначально

3)240/8= 30 мест в каждом автобусе первоначально

Ответ 30 мест

2 способ алгебраический:

пусть х мест было в автобусе первоначально. Тогда после добавления стало х+15. Всего мест в 8 автобусах 8*(х+15) и разместилось бы 360 человек. 
составим уравнение:

$\displaystyle 8*(x+15)=360 8x+120=360 8x=360-120 8x=240 x=240:8 x=30$

ответ : в автобусе было  30 мест первоначально

Answer 2

Problem Statement

Для отправки детей в летний лагерь было подано 8 одинаковых автобусов. Если бы в каждом автобусе было на 15 мест больше, то в них смогли бы разместиться 360 человек. Сколько мест было в каждом из автобусов? Постарайтесь решить задачу двумя способами: арифметически и алгебраически!

Solution

To solve this problem, we can use both arithmetic and algebraic methods.

Arithmetic Solution

Let's use the arithmetic method to solve the problem.

Given: - 8 identical buses - If each bus had 15 more seats, they could accommodate 360 people

To find the number of seats in each bus, we can subtract the additional 15 seats from the total number of seats when accommodating 360 people.

Let's calculate it step by step:

1. Calculate the total number of seats in the buses when accommodating 360 people: - Total seats = 360

2. Calculate the total number of seats in the buses without the additional 15 seats: - Total seats without additional seats = Total seats - (Number of buses * Additional seats per bus) - Total seats without additional seats = 360 - (8 * 15)

3. Calculate the number of seats in each bus: - Number of seats in each bus = Total seats without additional seats / Number of buses

Let's calculate the solution:

1. Total seats without additional seats = 360 - (8 * 15) = 360 - 120 = 240 2. Number of seats in each bus = 240 / 8 = 30

Therefore, each bus originally had 30 seats.

Algebraic Solution

Now let's solve the problem using an algebraic approach.

Let's assume the number of seats in each bus is represented by the variable 'x'.

Given: - 8 identical buses - If each bus had 15 more seats, they could accommodate 360 people

We can set up the following equation:

8(x + 15) = 360

Let's solve the equation step by step:

1. Distribute the 8 to both terms inside the parentheses: - 8x + 8(15) = 360

2. Simplify the equation: - 8x + 120 = 360

3. Subtract 120 from both sides of the equation: - 8x = 360 - 120 - 8x = 240

4. Divide both sides of the equation by 8 to solve for x: - x = 240 / 8 - x = 30

Therefore, each bus originally had 30 seats.

Both the arithmetic and algebraic methods yield the same result: each bus originally had 30 seats.

Conclusion

Each of the 8 identical buses originally had 30 seats.