To find the total number of contestants, [tex]\( C \)[/tex], who audition in [tex]\( h \)[/tex] hours, let's break down the problem step by step.
1. Understand the Rate: We know that 32 contestants audition each hour. This means:
- In 1 hour, 32 contestants are auditioned.
- In 2 hours, [tex]\( 32 \times 2 \)[/tex] contestants are auditioned.
- In 3 hours, [tex]\( 32 \times 3 \)[/tex] contestants are auditioned.
- Generally, in [tex]\( h \)[/tex] hours, [tex]\( 32 \times h \)[/tex] contestants are auditioned.
2. Form the Equation:
To find the total number of contestants, [tex]\( C \)[/tex], we multiply the number of contestants auditioned per hour (which is 32) by the number of hours [tex]\( h \)[/tex].
Therefore, the equation is:
[tex]\[
C = 32 \times h
\][/tex]
Or more simply:
[tex]\[
C = 32h
\][/tex]
3. Match with Given Options:
- Option A: [tex]\(\frac{32}{h} = C\)[/tex] implies dividing 32 by the number of hours, which is incorrect as it does not represent our rate of 32 contestants per hour.
- Option B: [tex]\(32h = C\)[/tex] correctly matches our derived equation.
- Option C: [tex]\(32 + h = C\)[/tex] implies adding 32 and [tex]\( h \)[/tex], which doesn't make sense in the context of multiplication for repeated hourly auditions.
- Option D: [tex]\(\frac{h}{32} = C\)[/tex] implies dividing the number of hours by 32, which is incorrect in the context of the problem.
Therefore, the correct equation that represents the total number of contestants auditioned in [tex]\( h \)[/tex] hours is:
[tex]\[
\boxed{32h = C}
\][/tex]
