Question

Составте систему уравнения и решите способом сложения.Среднее арифметическое двух чисел равно 175. Если первое число разделить на второе, то частное будет рано 3 , а остаток 30 . Найдите эти два числа....

Answer 1

х-первое число

у - второе число

х:у=3(ост.30)

 

х=3у+30

(х+у):2=175, подставим значение х во второе уравнение

3у+30+у/2=175 , общий знаменатель 2

4у=320

у=80 - второе число

80*3+30=270 - первое число

Провкрка:

(80+270):2=175

 

Answer 2

Problem Analysis

We are given the following information: - The average of two numbers is 175. - When the first number is divided by the second number, the quotient is 3 and the remainder is 30.

We need to find these two numbers.

Mathematical Formulation

Let's assume the two numbers are x and y.

From the given information, we can form the following equations: 1. The average of two numbers is 175: (x + y) / 2 = 175

2. When the first number is divided by the second number, the quotient is 3 and the remainder is 30: x = 3y + 30

We can solve these equations simultaneously to find the values of x and y.

Solving the Equations

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

From equation 2, we can express x in terms of y: x = 3y + 30

Substituting this value of x in equation 1, we get: (3y + 30 + y) / 2 = 175

Simplifying the equation: 4y + 30 = 350 4y = 350 - 30 4y = 320 y = 320 / 4 y = 80

Substituting the value of y back into equation 2, we can find x: x = 3(80) + 30 x = 240 + 30 x = 270

Therefore, the two numbers are x = 270 and y = 80.

Answer

The two numbers are 270 and 80.