Find the value of A when the arithmetic mean of A+7 and A+3 is 3a+9

We are given the arithmetic mean of \( A + 7 \) and \( A + 3 \), and it equals \( 3A + 9 \). To find the value of \( A \), let's break it down step by step.

### Step 1: Formula for Arithmetic Mean
The arithmetic mean of two numbers \( x \) and \( y \) is given by:

\[
\text{Mean} = \frac{x + y}{2}
\]

In this case, the two numbers are \( A + 7 \) and \( A + 3 \). So, the arithmetic mean is:

\[
\frac{(A + 7) + (A + 3)}{2}
\]

### Step 2: Simplify the Expression
Simplifying the numerator:

\[
(A + 7) + (A + 3) = 2A + 10
\]

So, the arithmetic mean becomes:

\[
\frac{2A + 10}{2}
\]

Simplify the fraction:

\[
A + 5
\]

### Step 3: Set Equal to the Given Expression
We are told that this arithmetic mean is equal to \( 3A + 9 \). Therefore:

\[
A + 5 = 3A + 9
\]

### Step 4: Solve for \( A \)
To solve for \( A \), subtract \( A \) from both sides:

\[
5 = 2A + 9
\]

Next, subtract 9 from both sides:

\[
-4 = 2A
\]

Finally, divide by 2:

\[
A = -2
\]

### Conclusion:
The value of \( A \) is \( -2 \).

---

Would you like more details or have any questions?

Here are 5 related questions:
1. How is the arithmetic mean used in statistics?
2. What are other types of means besides arithmetic mean?
3. Can you solve a similar problem but with different numbers?
4. How do you verify the correctness of a mean calculation?
5. What is the relationship between mean and median in data sets?

**Tip:** In arithmetic mean problems, always ensure the terms are correctly simplified before proceeding with comparisons.

Find the value of A when the arithmetic mean of A+7 and A+3 is 3A+9

Learn how to solve for A in an equation involving the arithmetic mean. This step-by-step guide covers algebraic manipulation and linear equations, suitable for students in Grades 8-10. Discover key formulas such as the arithmetic mean and linear equation solving methods.

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