Sure, let's solve this problem step-by-step.
### Given Information:
1. Arithmetic Mean: 25
2. Number of arithmetic means required: 9
### Calculation Details:
1. Step 1: Understand what the arithmetic mean of two numbers means.
If we have two numbers, say [tex]\( X \)[/tex] and [tex]\( Y \)[/tex], their arithmetic mean is calculated as:
[tex]\[
\text{Arithmetic Mean} = \frac{X + Y}{2}
\][/tex]
2. Step 2: Given that the arithmetic mean of these two numbers is 25, we can set up the equation as:
[tex]\[
\frac{X + Y}{2} = 25
\][/tex]
3. Step 3: Multiply both sides by 2 to eliminate the fraction:
[tex]\[
X + Y = 50
\][/tex]
So, the sum of the two numbers is:
[tex]\[
X + Y = 50
\][/tex]
4. Step 4: We are required to find the two numbers. Since we only have the sum of the numbers and no other constraints, there are infinite pairs of numbers that can satisfy the equation [tex]\( X + Y = 50 \)[/tex]. Some possible pairs include:
- [tex]\( (X, Y) = (0, 50) \)[/tex]
- [tex]\( (X, Y) = (10, 40) \)[/tex]
- [tex]\( (X, Y) = (20, 30) \)[/tex]
And so on.
### Summary:
1. Arithmetic Mean (A): [tex]\( 25 \)[/tex]
2. Sum of the two numbers (X + Y): [tex]\( 50 \)[/tex]
3. Number of Arithmetic Means: [tex]\( 9 \)[/tex]
The two required numbers can be any pair that adds up to 50, such as [tex]\( (0, 50) \)[/tex], [tex]\( (10, 40) \)[/tex], [tex]\( (20, 30) \)[/tex], etc.
