find two number of the sum of 65. twice the lesser number is 10 more than the greater number. Find the numbers

Let's solve this step by step. 

We need to find two numbers, say \( x \) and \( y \), where \( x \) is the lesser number and \( y \) is the greater number. According to the problem, we have two conditions:

1. The sum of the two numbers is 65:  
   \[
   x + y = 65
   \]

2. Twice the lesser number is 10 more than the greater number:  
   \[
   2x = y + 10
   \]

Now, let's solve these equations simultaneously.

### Step 1: Express \( y \) from the first equation
From the first equation \( x + y = 65 \), we can express \( y \) as:
\[
y = 65 - x
\]

### Step 2: Substitute \( y \) into the second equation
Substitute \( y = 65 - x \) into the second equation \( 2x = y + 10 \):
\[
2x = (65 - x) + 10
\]

### Step 3: Simplify and solve for \( x \)
Now, simplify the equation:
\[
2x = 65 - x + 10
\]
\[
2x + x = 75
\]
\[
3x = 75
\]
\[
x = \frac{75}{3} = 25
\]

So, the lesser number \( x \) is 25.

### Step 4: Find \( y \) using the value of \( x \)
Substitute \( x = 25 \) back into the equation \( y = 65 - x \):
\[
y = 65 - 25 = 40
\]

So, the greater number \( y \) is 40.

### Final Answer
The two numbers are **25** and **40**.

Would you like more details or have any other questions?

Here are five related questions:
1. How do you solve simultaneous linear equations?
2. What are the methods to solve quadratic equations?
3. How do you check if a solution to a system of equations is correct?
4. What are some examples of word problems involving systems of equations?
5. How can linear equations be applied in real-life situations?

**Tip:** Always double-check your solution by substituting the numbers back into the original equations.

Explore how to solve a problem involving finding two numbers with a sum of 65. Understand the method to solve simultaneous linear equations step-by-step. Suitable for students in Grades 7-9.

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