Question

Если Петя отдаст 18 почтовых марок Коле и 10 марок Мите, то марок у всех троих станет поровну. Сколько марок у каждого из ребят, если всего у них 90 марок?

Answer 1

30 марок у каждого
90/3=30

Answer 2

Problem Analysis

To solve this problem, we need to determine how many stamps each of the three boys, Petya, Kolya, and Mitya, have if they distribute a total of 90 stamps among themselves. According to the given information, if Petya gives 18 stamps to Kolya and 10 stamps to Mitya, then the number of stamps will be equal for all three boys.

Solution

Let's assume that Petya initially has x stamps, Kolya has y stamps, and Mitya has z stamps. We can set up the following equation based on the given information:

x - 18 = y + 18 (Petya gives 18 stamps to Kolya)

x - 10 = z + 10 (Petya gives 10 stamps to Mitya)

Since the total number of stamps is 90, we can also set up the equation:

x + y + z = 90

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

Solution Steps

1. Substitute the first equation into the third equation to eliminate x:

(y + 18) + y + z = 90

Simplifying, we get:

2y + z = 72 (Equation 4)

2. Substitute the second equation into the third equation to eliminate x:

(z + 10) + y + z = 90

Simplifying, we get:

2z + y = 80 (Equation 5)

3. Now we have a system of two equations (Equations 4 and 5) with two variables (y and z). We can solve this system of equations to find the values of y and z.

4. Subtract Equation 4 from Equation 5 to eliminate y:

(2z + y) - (2y + z) = 80 - 72

Simplifying, we get:

z - y = 8 (Equation 6)

5. Add Equation 4 and Equation 6 to eliminate y:

(2y + z) + (z - y) = 72 + 8

Simplifying, we get:

3z = 80

Solving for z, we find:

z = 80 / 3 = 26.67

6. Since the number of stamps must be a whole number, we can round z to the nearest whole number:

z ≈ 27

7. Substitute the value of z back into Equation 6 to find y:

27 - y = 8

Solving for y, we find:

y = 27 - 8 = 19

8. Finally, substitute the values of y and z into the third equation to find x:

x + 19 + 27 = 90

Simplifying, we get:

x = 90 - 46 = 44

Answer

Therefore, Petya has 44 stamps, Kolya has 19 stamps, and Mitya has 27 stamps.

Please note that the solution involves rounding, so the values may not be exact integers.