To solve for [tex]\( k \)[/tex] in terms of [tex]\( h \)[/tex] given the equation [tex]\( h = \frac{20k + 3}{7} \)[/tex], we need to isolate [tex]\( k \)[/tex]. Here’s a step-by-step solution:
1. Start with the given equation:
[tex]\[
h = \frac{20k + 3}{7}
\][/tex]
2. Multiply both sides by 7 to eliminate the denominator:
[tex]\[
7h = 20k + 3
\][/tex]
3. Isolate the term involving [tex]\( k \)[/tex] by subtracting 3 from both sides:
[tex]\[
7h - 3 = 20k
\][/tex]
4. Solve for [tex]\( k \)[/tex] by dividing both sides by 20:
[tex]\[
k = \frac{7h - 3}{20}
\][/tex]
Now, we have expressed [tex]\( k \)[/tex] in terms of [tex]\( h \)[/tex] as:
[tex]\[
k = \frac{7h - 3}{20}
\][/tex]
Comparing this to the given form [tex]\( k = \frac{ah + b}{c} \)[/tex], we can identify the constants [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:
[tex]\[
a = 7, \quad b = -3, \quad c = 20
\][/tex]
Finally, we need to find the sum of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:
[tex]\[
a + b + c = 7 + (-3) + 20 = 7 - 3 + 20 = 24
\][/tex]
Therefore, the sum of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] is:
[tex]\[
\boxed{24}
\][/tex]
