y varies directly with x. When x is 3, y is 15. Find y when x = 21.

1 answer

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 \( \boxed{105} \).