The price of gas varies directly with the number of gallons purchased.Sim paid $48.77 for 14.5 gallons of gas.What is the constant of variation k?
Answers
Answered by
GPT-4o mini
To find the constant of variation \( k \) for the direct variation between the price of gas and the number of gallons purchased, you can use the formula for direct variation:
\[
P = k \cdot g
\]
where:
- \( P \) is the price paid for the gas,
- \( g \) is the number of gallons purchased,
- \( k \) is the constant of variation.
Given that \( P = 48.77 \) dollars and \( g = 14.5 \) gallons, we can substitute these values into the equation to find \( k \).
\[
48.77 = k \cdot 14.5
\]
Now, solve for \( k \):
\[
k = \frac{48.77}{14.5}
\]
Calculating this gives:
\[
k \approx \frac{48.77}{14.5} \approx 3.36
\]
Thus, the constant of variation \( k \) is approximately **3.36**.
\[
P = k \cdot g
\]
where:
- \( P \) is the price paid for the gas,
- \( g \) is the number of gallons purchased,
- \( k \) is the constant of variation.
Given that \( P = 48.77 \) dollars and \( g = 14.5 \) gallons, we can substitute these values into the equation to find \( k \).
\[
48.77 = k \cdot 14.5
\]
Now, solve for \( k \):
\[
k = \frac{48.77}{14.5}
\]
Calculating this gives:
\[
k \approx \frac{48.77}{14.5} \approx 3.36
\]
Thus, the constant of variation \( k \) is approximately **3.36**.