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Sagot :
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]
### 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]
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