To solve the equation [tex]\( C = \frac{1}{3} h (r + k) \)[/tex] for [tex]\( r \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
C = \frac{1}{3} h (r + k)
\][/tex]
2. Isolate the term with [tex]\( r \)[/tex] on one side:
Multiply both sides of the equation by 3 to get rid of the fraction:
[tex]\[
3C = h (r + k)
\][/tex]
3. Solve for [tex]\( r \)[/tex]:
Divide both sides by [tex]\( h \)[/tex] to isolate [tex]\( r + k \)[/tex]:
[tex]\[
\frac{3C}{h} = r + k
\][/tex]
4. Subtract [tex]\( k \)[/tex] from both sides to solve for [tex]\( r \)[/tex]:
[tex]\[
r = \frac{3C}{h} - k
\][/tex]
Thus, the solution for [tex]\( r \)[/tex] in terms of [tex]\( C \)[/tex], [tex]\( h \)[/tex], and [tex]\( k \)[/tex] is:
[tex]\[
r = \frac{3C}{h} - k
\][/tex]
So, the answer is:
[tex]\[
r = \boxed{\frac{3C}{h} - k}
\][/tex]
