Question
Find the weighted average of points P=5 and Q=25 on a number line, given the ratio of 2:3 .(1 point)
Answers
GPT-4o mini
To find the weighted average of points \( P = 5 \) and \( Q = 25 \) in the ratio \( 2:3 \), we can use the formula for the weighted average:
\[
\text{Weighted Average} = \frac{(w_1 \cdot x_1) + (w_2 \cdot x_2)}{w_1 + w_2}
\]
where:
- \( w_1 \) and \( w_2 \) are the weights,
- \( x_1 \) and \( x_2 \) are the values.
In this case, we have:
- \( w_1 = 2 \) (weight for point \( P \)),
- \( x_1 = 5 \) (value of point \( P \)),
- \( w_2 = 3 \) (weight for point \( Q \)),
- \( x_2 = 25 \) (value of point \( Q \)).
Now, substituting these values into the formula:
\[
\text{Weighted Average} = \frac{(2 \cdot 5) + (3 \cdot 25)}{2 + 3}
\]
Calculating the numerator:
\[
(2 \cdot 5) + (3 \cdot 25) = 10 + 75 = 85
\]
Calculating the denominator:
\[
2 + 3 = 5
\]
Now, putting it all together:
\[
\text{Weighted Average} = \frac{85}{5} = 17
\]
Therefore, the weighted average of points \( P \) and \( Q \) in the ratio \( 2:3 \) is \( \boxed{17} \).
\[
\text{Weighted Average} = \frac{(w_1 \cdot x_1) + (w_2 \cdot x_2)}{w_1 + w_2}
\]
where:
- \( w_1 \) and \( w_2 \) are the weights,
- \( x_1 \) and \( x_2 \) are the values.
In this case, we have:
- \( w_1 = 2 \) (weight for point \( P \)),
- \( x_1 = 5 \) (value of point \( P \)),
- \( w_2 = 3 \) (weight for point \( Q \)),
- \( x_2 = 25 \) (value of point \( Q \)).
Now, substituting these values into the formula:
\[
\text{Weighted Average} = \frac{(2 \cdot 5) + (3 \cdot 25)}{2 + 3}
\]
Calculating the numerator:
\[
(2 \cdot 5) + (3 \cdot 25) = 10 + 75 = 85
\]
Calculating the denominator:
\[
2 + 3 = 5
\]
Now, putting it all together:
\[
\text{Weighted Average} = \frac{85}{5} = 17
\]
Therefore, the weighted average of points \( P \) and \( Q \) in the ratio \( 2:3 \) is \( \boxed{17} \).