Question

Сумма двух чисел равна 150, если от большего числа отнять 7\32 его и прибавить к меньшему числу, то оба числа станут равными. Найдите эти числа. ПОМОГИТЕ!!!!!!! СРОЧНО!!!!!!! за правильный ответ дам 50 баллов

Answer 1

Ответ: 96 и 54

Пошаговое объяснение:

Пусть большее число х

Тогда меньшее у

х + у = 150

х - 7/32 х = 7/32 х + у

х = 150 - у

150 - у - 7/32 ( 150 - у) = 7/32 ( 150 - у) + у

Решим второе уравнение из системы

150 - у - 525/16 + 7/32 у = 525/16 - 7/32 у + у

- у + 7/32 у + 7/32 у - у = 525/16 + 525/16 - 150

-2у + 14/32 у = 1050/16 - 150

-2у + 7/16 у = 525/8 - 150

- 1целая 16/16 у + 7/16 у = 65целых 5/8 - 149целых 8/8

- 1целая 9/16 у = - 84целых 3/8

у = - 84целых 3/8 : ( - 1целая 9/16)

у = - 675/8 : ( - 25/16 )

у = - 675/8 * ( - 16/25 )

у = - 27/1 * ( - 2/1 )

у = -27 * (-2)

у = 54

Теперь значение у подставим в первое

х = 150-54

х = 96

Значит большее число равно 96, а меньшее 54

Answer 2

Problem Analysis

We are given that the sum of two numbers is 150. If we subtract 7/32 of the larger number and add it to the smaller number, the two numbers will be equal. We need to find these two numbers.

Solution

Let's assume the larger number is x and the smaller number is y.

According to the given information, we can form the following equations:

1. x + y = 150 (the sum of the two numbers is 150) 2. x - (7/32)x + y = y (if we subtract 7/32 of the larger number from it and add it to the smaller number, the two numbers will be equal)

To solve this system of equations, we can substitute the value of y from equation 1 into equation 2.

Substituting y = 150 - x into equation 2, we get:

x - (7/32)x + (150 - x) = 150 - x

Simplifying the equation:

x - (7/32)x + 150 - x = 150 - x

- (7/32)x + 150 = 0

- (7/32)x = -150

Multiplying both sides by -32/7 to isolate x:

x = (150 * 32) / 7

Evaluating the expression:

x = 685.714

Now, we can substitute the value of x into equation 1 to find y:

685.714 + y = 150

y = 150 - 685.714

y = -535.714

Therefore, the two numbers are approximately 685.714 and -535.714.

Please note that these calculations are approximate due to rounding.