Question

В трёх коробках лежат пряники. В первой пряников на 6 меньше, чем в двух других вместе, а во второй-на 10 меньше, чем в первой и третьей вместе. Сколько пряников в третьей коробке?

Answer 1

Во 2 коробке = в        пряников
в 3 коробке = а          пряников
по условию в   1 коробке  = a+b-6  пряников
и во 2 коробке = а+(а+в-6)-10 
 тогда а+(а+в-6)-10=в
2а=16
а=8  пряников в 3 коробке

Answer 2

Problem Analysis

We are given three boxes of gingerbread cookies. The number of cookies in the first box is 6 less than the sum of the cookies in the other two boxes. The number of cookies in the second box is 10 less than the sum of the cookies in the first and third boxes. We need to determine the number of cookies in the third box.

Solution

Let's assume the number of cookies in the first, second, and third boxes are represented by variables x, y, and z respectively.

According to the given information: 1. The number of cookies in the first box is 6 less than the sum of the cookies in the other two boxes: x = (y + z) - 6. 2. The number of cookies in the second box is 10 less than the sum of the cookies in the first and third boxes: y = (x + z) - 10.

We can solve these two equations to find the values of x and y. Then, we can substitute these values into the first equation to find the value of z.

Let's solve the equations step by step:

1. Substitute the value of y from the second equation into the first equation: x = ((x + z) - 10 + z) - 6.

2. Simplify the equation: x = 2x + 2z - 16.

3. Rearrange the equation: x - 2x = 2z - 16.

4. Simplify further: -x = 2z - 16.

5. Rearrange the equation: x = 16 - 2z.

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

6. Substitute the value of x into the second equation: y = ((16 - 2z) + z) - 10.

7. Simplify the equation: y = 16 - z - 10.

8. Simplify further: y = 6 - z.

Now, we have two equations: - Equation 1: x = 16 - 2z. - Equation 2: y = 6 - z.

We can substitute these equations into the given information to find the value of z.

9. The number of cookies in the first box is 6 less than the sum of the cookies in the other two boxes: x = (y + z) - 6.

10. Substitute the values of x and y from the equations: 16 - 2z = (6 - z) + z - 6.

11. Simplify the equation: 16 - 2z = 6 - 6.

12. Simplify further: 16 - 2z = 0.

13. Rearrange the equation: 2z = 16.

14. Solve for z: z = 16 / 2.

15. Calculate the value of z: z = 8.

Therefore, there are 8 gingerbread cookies in the third box.

Answer

There are 8 gingerbread cookies in the third box.