Question

Гриша загадал два числа сумма - утроенного первого числа и второго равна 242 а удвоенная сумма первого и второго чисел равна 200 чему равна разность большего и меньшего из загаданных гришей чисел

Answer 1

Пусть первое число -х
          второе число-у
Тогда составим систему из 2-х уравнений:
1)3х+у=242                 2)2(х+у)=200
Решаем 2-ое уравнение:
2(х+у)=200
х+у=200/2
х+у=100
х=100-у
Подставляем результат в 1-ое уравнение:
3(100-у)+у=242
300-3у+у=242
300-2у=242
2у=300-242
2у=58
у=58/2
у=29
х=100-у
х=100-29
х=71
х-у=71-29
х-у=42
Ответ: разность чисел 42.
                                      

Answer 2

Только в  приведенном решении надо от 71 отнять 29.
71 - 29 = 42
Ответ: 42

Answer 3

Problem Analysis

Grisha has chosen two numbers, and we need to find the difference between the larger and smaller of these two numbers. We are given two equations to work with: 1. The tripled first number plus the second number equals 242. 2. The doubled sum of the two numbers equals 200.

Let's solve this problem step by step.

Solution

Let's assume the first number chosen by Grisha is x and the second number is y.

From the first equation, we know that the tripled first number plus the second number equals 242. Mathematically, this can be represented as:

3x + y = 242 From the second equation, we know that the doubled sum of the two numbers equals 200. Mathematically, this can be represented as:

2(x + y) = 200 Now, we have a system of two equations with two variables. We can solve this system of equations to find the values of x and y.

Let's solve the system of equations using the substitution method:

1. Solve equation 2 for x: 2(x + y) = 200 2x + 2y = 200 2x = 200 - 2y x = (200 - 2y) / 2 x = 100 - y 2. Substitute the value of x from equation 1 into equation 2: 3x + y = 242 3(100 - y) + y = 242 300 - 3y + y = 242 -2y = -58 y = 29 3. Substitute the value of y into equation 1 to find x: 3x + y = 242 3x + 29 = 242 3x = 242 - 29 3x = 213 x = 71 Now we have the values of x and y. The first number chosen by Grisha is 71, and the second number is 29.

To find the difference between the larger and smaller of these two numbers, we subtract the smaller number from the larger number:

Difference = Larger number - Smaller number Difference = 71 - 29 Difference = 42

Therefore, the difference between the larger and smaller of the two numbers chosen by Grisha is 42.

I hope this helps! Let me know if you have any further questions.