Question

Ваня и Петя спорили о своих марках. Ваня говорит Петру Отдай ты мне одну марку, тога у меня будет ровно вдвое больше марок чем у тебя. А Петя ему отвечает Лучше ты мне отдай одну марку тогда у нас марок будет поровну. СКолько марок было у каждого?

Answer 1

Ответ:

5и7

5-1=4

7+1=8

4×2=8

7-1=6

5+1=6

6=6

Answer 2

Ответ:

У Вани 7 марок. У Пети 5 марок.

Пошаговое объяснение:

Пусть у Вани х марок. У Пети у марок.

Тогда, если Петя отдаст 1  одну марку Ване, то у Вани  будет ровно вдвое больше марок чем у Пети

2(у-1) = х+1

Если Ваня отдаст 1  одну марку Пете, то у Вани и Пети   будет поровну

х-1=у+1

Составим систему уравнений

{2(у-1) = х+1;    {2у-3= х;

{х-1=у+1           {х=у+2

Приравняем икс, и решим уравнение относительно у.

2у-3=у+2

2у-у=2+3

у=5

х=у+2

х=5+2

х=7

У Вани 7 марок. У Пети 5 марок.

1) если Петя отдаст марку Ване, у Вани станет в 2 раза больше, чем у Пети

4-1=4

7+1=8

8= 4*2

2) если Ваня отдаст марку Пете,  у них станет поровну

7-1=6

5+1=6

Answer 3

Problem Analysis

Vanya and Petya are arguing about their stamps. Vanya claims that if Petya gives him one stamp, then Vanya will have exactly twice as many stamps as Petya. Petya, on the other hand, suggests that if Vanya gives him one stamp, then they will have an equal number of stamps. We need to determine how many stamps each person had initially.

Solution

Let's assume that Vanya initially had x stamps and Petya had y stamps.

According to Vanya's claim, if Petya gives him one stamp, then Vanya will have twice as many stamps as Petya. Mathematically, this can be represented as:

x + 1 = 2(y - 1)

According to Petya's claim, if Vanya gives him one stamp, then they will have an equal number of stamps. Mathematically, this can be represented as:

y + 1 = x - 1

We can solve this system of equations to find the values of x and y.

Solving the System of Equations

Let's solve the system of equations using substitution:

From Petya's claim, we have:

y + 1 = x - 1

Rearranging the equation, we get:

x = y + 2

Substituting this value of x into Vanya's claim, we have:

(y + 2) + 1 = 2(y - 1)

Simplifying the equation:

y + 3 = 2y - 2

Bringing all the terms to one side:

2y - y = 3 + 2

Simplifying further:

y = 5

Substituting this value of y back into the equation x = y + 2, we have:

x = 5 + 2 = 7

Therefore, Vanya initially had 7 stamps and Petya initially had 5 stamps.

Answer

Vanya initially had 7 stamps and Petya initially had 5 stamps.