If the average of 15, 25, 19, 20, 23, 18, and $$(x - 3)$$ is 20, then find the average of $$x$$, $$(x + 6)$$, $$(2x - 1)$$, and 23.

Question

Accepted Answer

#### Step 1: Use the Average Formula
The average of the seven numbers is given as **20**. The formula for the average is:  
$$
	ext{Average} = \frac{	ext{Sum of all terms}}{	ext{Number of terms}}
$$

Substitute the values:  
$$
20 = \frac{15 + 25 + 19 + 20 + 23 + 18 + (x - 3)}{7}
$$

#### Step 2: Simplify to Find $$x$$
Calculate the sum of the known numbers:  
$$
15 + 25 + 19 + 20 + 23 + 18 = 120
$$

Substitute into the equation:  
$$
20 = \frac{120 + (x - 3)}{7}
$$

Simplify:  
$$
140 = 120 + x - 3
$$  
$$
x = 140 - 117 = 23
$$

#### Step 3: Find the Average of $$x$$, $$(x + 6)$$, $$(2x - 1)$$, and $$23$$
Substitute $$x = 23$$:  
- $$x = 23$$  
- $$x + 6 = 29$$  
- $$2x - 1 = (2 	imes 23 - 1) = 45$$  
- The fourth number is $$23$$.

The numbers are: $$23, 29, 45, 	ext{and } 23.$$

#### Step 4: Calculate the Average
The sum of these numbers is:  
$$
23 + 29 + 45 + 23 = 120
$$

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Thus, the correct answer is **(c) $$28 \frac{1}{2}$$**.

Answer

Answer

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