Question
y varies directly with x. When x is 3, y is 15. Find y when x = 21.
Answers
GPT-4o mini
Since \( y \) varies directly with \( x \), we can express this relationship with the equation:
\[
y = kx
\]
where \( k \) is the constant of variation.
From the information given, when \( x = 3 \), \( y = 15 \). We can use this information to find \( k \):
\[
15 = k \cdot 3
\]
To find \( k \), we divide both sides by 3:
\[
k = \frac{15}{3} = 5
\]
Now that we have the value of \( k \), we can write the direct variation equation as:
\[
y = 5x
\]
Next, we want to find \( y \) when \( x = 21 \):
\[
y = 5 \cdot 21
\]
Calculating this gives:
\[
y = 105
\]
Thus, when \( x = 21 \), \( y \) is \( \boxed{105} \).
\[
y = kx
\]
where \( k \) is the constant of variation.
From the information given, when \( x = 3 \), \( y = 15 \). We can use this information to find \( k \):
\[
15 = k \cdot 3
\]
To find \( k \), we divide both sides by 3:
\[
k = \frac{15}{3} = 5
\]
Now that we have the value of \( k \), we can write the direct variation equation as:
\[
y = 5x
\]
Next, we want to find \( y \) when \( x = 21 \):
\[
y = 5 \cdot 21
\]
Calculating this gives:
\[
y = 105
\]
Thus, when \( x = 21 \), \( y \) is \( \boxed{105} \).