Say my x is on avg 17.07 and contributes 41% to the total. The current total AVG is 25.57 . If x would increase from contribution from 41 to 57%, what would the new overall avg be?

To find the new overall average, we can approach this problem by setting up a weighted average formula.

### Given Information
1. The average value of \( x \) is 17.07.
2. \( x \) currently contributes 41% (0.41) to the total.
3. The current total average is 25.57.
4. We want to find the new total average if \( x \)'s contribution increases to 57% (0.57).

Let:
- \( A \) represent the average of the "other" contributors (the components other than \( x \)).

### Step-by-Step Solution

#### Step 1: Determine \( A \) based on the current average
Using the current weights and averages:
\[
0.41 \times 17.07 + 0.59 \times A = 25.57
\]
Solving for \( A \):
\[
0.41 \times 17.07 = 7.0047
\]
\[
0.59 \times A = 25.57 - 7.0047
\]
\[
A = \frac{18.5653}{0.59} = 31.47
\]

So, the average of the other contributors \( A \) is approximately 31.47.

#### Step 2: Calculate the new total average with \( x \) contributing 57%
With \( x \) now contributing 57% (0.57) and the "other" contributors 43% (0.43):
\[
\text{New Total Average} = (0.57 \times 17.07) + (0.43 \times 31.47)
\]
Calculating each part:
\[
0.57 \times 17.07 = 9.7299
\]
\[
0.43 \times 31.47 = 13.5321
\]
\[
\text{New Total Average} = 9.7299 + 13.5321 = 23.262
\]

### Answer
The new overall average, if \( x \)'s contribution increases to 57%, would be approximately **23.26**.

Would you like further details or have any questions about this? 

---

1. What would happen to the overall average if \( x \) contributed less than 41%?
2. How would changes in \( x \)’s average impact the overall total average?
3. How do weighted averages work in broader statistical contexts?
4. What happens if the contribution percentages do not sum up to 100%?
5. Can this method be used to estimate future changes in weighted averages?

**Tip:** When dealing with weighted averages, it helps to isolate the unknown variables for simpler calculation.

Say my x is on avg 17.07 and contributes 41% to the total. The current total AVG is 25.57. If x would increase from contribution from 41 to 57%, what would the new overall avg be?

Learn how to find a new weighted average when the contribution percentage of one component changes. In this example, the average of x (17.07) shifts its contribution from 41% to 57%, affecting the overall average, initially 25.57. This solution explains the weighted average formula and step-by-step calculations.

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