Question

Брат и сестра собирали марки. У них вместе на 20 марок больше , чем у брата, и на 12 марок больше, чем у сестры. Сколько марок у каждого и сколько марок у них вместе?

Answer 1

У брата 12, у сестры 20

Answer 2

Problem Analysis

We are given that a brother and sister collected stamps. Together, they have 20 more stamps than the brother and 12 more stamps than the sister. We need to determine how many stamps each of them has and the total number of stamps they have together.

Solution

Let's assume that the brother has x stamps and the sister has y stamps.

According to the given information: - The total number of stamps they have together is 20 more than what the brother has: x + y = x + 20. - The total number of stamps they have together is 12 more than what the sister has: x + y = y + 12.

To solve this system of equations, we can subtract the second equation from the first equation to eliminate the y variable:

(x + y) - (x + y) = (x + 20) - (y + 12).

Simplifying this equation gives us:

0 = x + 20 - y - 12.

Combining like terms, we get:

0 = x - y + 8.

Rearranging the equation, we have:

x - y = -8.

Now, we have a system of two equations with two variables:

1. x + y = x + 20 2. x - y = -8

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

Solving the System of Equations

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination.

Adding the two equations together, we get:

(x + y) + (x - y) = (x + 20) + (-8).

Simplifying this equation gives us:

2x = x + 12.

Subtracting x from both sides, we have:

x = 12.

Now, we can substitute the value of x back into one of the original equations to find the value of y.

Using the equation x + y = x + 20, we substitute x = 12:

12 + y = 12 + 20.

Simplifying this equation gives us:

y = 20.

Therefore, the brother has 12 stamps and the sister has 20 stamps. The total number of stamps they have together is 32.

Answer

The brother has 12 stamps, the sister has 20 stamps, and they have 32 stamps together.