Question

S varies directly as T.

If S is 20 when T is 4, then T is
when S is 30.

Answer 1

Since \( S \) varies directly as \( T \), we can express this relationship as:

\[
S = kT
\]

where \( k \) is the constant of proportionality.

Given that \( S = 20 \) when \( T = 4 \), we can find \( k \):

\[
20 = k(4)
\]

To solve for \( k \), divide both sides by 4:

\[
k = \frac{20}{4} = 5
\]

Now that we have the constant \( k = 5 \), we can use this to find \( T \) when \( S = 30 \):

Using the formula \( S = kT \):

\[
30 = 5T
\]

Now, solve for \( T \):

\[
T = \frac{30}{5} = 6
\]

Therefore, when \( S \) is 30, \( T \) is \( 6 \).