Question

Саша рассаживал солдатиков в машинки. Если он сажал в каждую машинку по 2 солдатика, то 4 солдатика оставались лишними, если по 3 солдатика, то одна машинка оставалась без солдатиков. Сколько было машинок и сколько солдатиков?

Answer 1

Для решения попробуем составить систему уравнений и решить их, обазначим общее количество солдатиков через "x", а количество машинок через "Y", тогда получим: 2Y+4=X: X/3=Y-1: в первом уравнении выразим "Y" получается 2Y=X-4 или Y=(X-4)/2: подставим первое во второе (X)/3=(X-4)/2-1 приводим к общему знаминателю это 6, получаем 2X=3X-12-6 или X=18 подставим в первое уравнение что получилось, 2Y+4=18 или Y=7; Ответ: Солдатиков 18, Машинок 7.

Answer 2

Problem Analysis

In this problem, we are given that Sasha is arranging soldiers into toy cars. If Sasha puts 2 soldiers in each car, 4 soldiers are left over. If Sasha puts 3 soldiers in each car, one car is left empty. We need to determine the number of cars and the number of soldiers.

Solution

Let's assume there are x cars and y soldiers.

If Sasha puts 2 soldiers in each car, then the total number of soldiers is 2x. We are given that 4 soldiers are left over, so we can write the equation:

2x + 4 = y If Sasha puts 3 soldiers in each car, then the total number of soldiers is 3x. We are given that one car is left empty, so we can write the equation:

3x = y + 1 We can solve this system of equations to find the values of x and y.

Solving the System of Equations

To solve the system of equations, we can use substitution or elimination. Let's use substitution.

From equation we can rewrite it as:

y = 3x - 1

Substituting this value of y into equation we get:

2x + 4 = 3x - 1

Simplifying the equation, we have:

x = 5

Substituting this value of x back into equation we get:

y = 3(5) - 1 = 14

Answer

Therefore, there are 5 cars and 14 soldiers.

Verification

Let's verify our answer using the given conditions.

If Sasha puts 2 soldiers in each car, then the total number of soldiers is 2(5) = 10. We are given that 4 soldiers are left over, which is true.

If Sasha puts 3 soldiers in each car, then the total number of soldiers is 3(5) = 15. We are given that one car is left empty, which is also true.

Therefore, our answer of 5 cars and 14 soldiers satisfies both conditions.

Conclusion

Sasha arranged 5 cars and 14 soldiers.