Question

ПОМОГИТЕ ПОЖАЛУЙСТА ДАЮ 100 БАЛЛОВ!!!!!!!!!!!!!!!! На покупу футбольного мяча два товарища истратили поровну: первый дал 1/8 своих денег, а второй 1/4 и ещё 1 руб. После покупки у второго осталось на 50 коп меньше чем у первого. Сколько было денег у каждого товарища первоначально и сколько стоит футбольный мяч?

Answer 1

Ответ:

У 1-го было х, он дал х/8 руб. У 2-го было у, он дал у/4 +1= (y+4)/4 руб.

x/8 = (y + 4)/4

У 1-го осталось 7х/8 руб, а у 2-го осталось у - (y+4)/4 = (3y-4)/4 руб.

И это на 50 коп = 1/2 руб. меньше, чем у 1-го.

7/8 - 1/2 = (Зу - 4)/4

Составляем систему. Оба уравнения умножаем

на 8

{ x = 2(y + 4)

{7x-4=2(3y-4)

Раскрываем скобки во 2 ур-нии.

[x=2y+8

{7x=6y -8 + 4 = 6y - 4

Подставляем 1 уравнение во 2 уравнение

7(2y+8)=6y-4

14y+56=6y-4

8y = -60

Объяснение:

Получается у < 0, чего не может быть. Вывод: в условии опечатка.

(взяла с другого ответа)

Answer 2

Problem Analysis

Two friends spent money equally to buy a football. The first friend spent 1/8 of his money, while the second friend spent 1/4 of his money plus an additional 1 ruble. After the purchase, the second friend had 50 kopeks less than the first friend. We need to determine how much money each friend initially had and the cost of the football.

Solution

Let's assume that the first friend initially had x rubles, and the cost of the football is y rubles.

According to the given information: - The first friend spent 1/8 of his money, which is (1/8)x rubles. - The second friend spent 1/4 of his money plus an additional 1 ruble, which is (1/4)x + 1 rubles. - After the purchase, the second friend had 50 kopeks (0.50 rubles) less than the first friend.

Based on these equations, we can set up the following equation:

(1/4)x + 1 + 0.50 = (1/8)x + y

Simplifying the equation:

(1/4)x - (1/8)x = y - 1 - 0.50

(1/8)x = y - 1.50

To solve for x and y, we need another equation. Let's use the fact that the second friend had 50 kopeks less than the first friend:

(1/4)x + 0.50 = (1/8)x

Simplifying the equation:

(1/4)x - (1/8)x = 0.50

(1/8)x = 0.50

Now we have a system of two equations:

(1/8)x = 0.50

(1/8)x = y - 1.50

Let's solve this system of equations to find the values of x and y.

Solution Steps

Step 1: Solve the equation (1/8)x = 0.50 for x: - Multiply both sides of the equation by 8 to eliminate the fraction: x = 0.50 * 8 = 4.

Step 2: Substitute the value of x into the equation (1/8)x = y - 1.50: - (1/8) * 4 = y - 1.50 - Simplify: 0.50 = y - 1.50 - Add 1.50 to both sides of the equation: 0.50 + 1.50 = y - Simplify: y = 2.

Therefore, the first friend initially had 4 rubles and the cost of the football is 2 rubles.

Answer

The first friend initially had 4 rubles and the second friend initially had 4 rubles. The cost of the football is 2 rubles.

Note: The solution assumes that the friends spent all of their money on the football and had no other sources of income or expenses.