Question

Знайдіть два числа, сума яких дорівнює 1000, а 30% першого на 200 більші за 20% другого. Помогите пожалуйста

Answer 1

Нехай перше число - х, а друге - у, тоді маємо систему рівнянь
х+у=1000
0,3х-0,2у=200

х=1000-у
0,3(1000-у)-0,2у=200

х=1000-у
300-0,3у-0,2у=200

х=1000-у
300-0,5у=200

х=1000-у
0,5у=100

х=1000-200
у=200

х=800
у=200

Answer 2

I can help you with your math problem. You are looking for two numbers, x and y, that satisfy the following conditions:

- x + y = 1000 - 0.3x - 0.2y = 200

To solve this system of equations, you can use the substitution method. First, isolate one variable in the first equation, for example:

- x = 1000 - y

Then, substitute this expression into the second equation and simplify:

- 0.3(1000 - y) - 0.2y = 200 - 300 - 0.3y - 0.2y = 200 - -0.5y = -100 - y = 200

Finally, plug this value of y into the first equation and solve for x:

- x = 1000 - y - x = 1000 - 200 - x = 800

Therefore, the two numbers are x = 800 and y = 200. You can check your answer by plugging these values into the original equations and verifying that they are true.

I hope this helps you understand how to solve this type of problem. If you need more help, you can visit some of these websites that explain the substitution method in more detail:

- [How to Solve Systems of Equations by Substitution](https://matematika.my-dict.ru/q/7791808_znajdit-dva-cisla-suma-akih-dorivnue/) - [Solving Systems of Equations Using Algebra Calculator](https://subject.com.ua/textbook/mathematics/9klas/16.html) - [Solving Systems of Equations by Substitution - Examples](https://subject.com.ua/textbook/mathematics/9klas_1/16.html)