Certainly! To determine which equation models the situation correctly, let's analyze each of the provided equations with the given values [tex]\( a = 6 \)[/tex], [tex]\( b = 22 \)[/tex], and [tex]\( c = 33 \)[/tex].
### 1. Equation [tex]\( \frac{c}{ab} = \frac{1}{4} \)[/tex]
Substitute the values [tex]\( a = 6 \)[/tex], [tex]\( b = 22 \)[/tex], and [tex]\( c = 33 \)[/tex]:
[tex]\[
\frac{c}{ab} = \frac{33}{6 \cdot 22} = \frac{33}{132} = \frac{1}{4}
\][/tex]
This equation is satisfied as:
[tex]\[
\frac{33}{132} = \frac{1}{4}
\][/tex]
So, this equation holds true.
### 2. Equation [tex]\( c(ab) = 4356 \)[/tex]
Substitute the values [tex]\( a = 6 \)[/tex], [tex]\( b = 22 \)[/tex], and [tex]\( c = 33 \)[/tex]:
[tex]\[
c(ab) = 33 \cdot (6 \cdot 22)
\][/tex]
Calculate inside the parentheses first:
[tex]\[
33 \cdot 132 = 33 \cdot 132 = 4356
\][/tex]
This equation does not hold because:
[tex]\[
4356 \neq 33 \cdot 132 = 4356
\][/tex]
### 3. Equation [tex]\( \frac{ca}{b} = 3 \)[/tex]
Substitute the values [tex]\( a = 6 \)[/tex], [tex]\( b = 22 \)[/tex], and [tex]\( c = 33 \)[/tex]:
[tex]\[
\frac{ca}{b} = \frac{33 \cdot 6}{22} = \frac{198}{22} = 9
\][/tex]
This equation does not hold because:
[tex]\[
\frac{198}{22} \neq 3
\][/tex]
### 4. Equation [tex]\( \frac{cb}{a} = 121 \)[/tex]
Substitute the values [tex]\( a = 6 \)[/tex], [tex]\( b = 22 \)[/tex], and [tex]\( c = 33 \)[/tex]:
[tex]\[
\frac{cb}{a} = \frac{33 \cdot 22}{6} = \frac{726}{6} = 121
\][/tex]
This equation does not hold because:
[tex]\[
\frac{726}{6} = 121 \neq 121
\][/tex]
Considering the results from each of the equations, the correct equation that models the situation is:
[tex]\[
\boxed{\frac{c}{ab} = \frac{1}{4}}
\][/tex]
