To determine the value of [tex]\( C \)[/tex] in the given table, follow these step-by-step calculations:
The table is represented as:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
\text{Pie} & 36 & 42 & 60 \\
\hline
\text{Cake} & D & 7 & B \\
\hline
\text{Total} & 42 & A & C \\
\hline
\end{array}
\][/tex]
### Step 1: Determine [tex]\( D \)[/tex]
From the Total column 1:
[tex]\[ 36 + D = 42 \][/tex]
[tex]\[ D = 42 - 36 \][/tex]
[tex]\[ D = 6 \][/tex]
### Step 2: Determine [tex]\( A \)[/tex]
From the Total column 2:
[tex]\[ 42 + 7 = A \][/tex]
[tex]\[ A = 42 + 7 \][/tex]
[tex]\[ A = 49 \][/tex]
### Step 3: Express [tex]\( C \)[/tex] in terms of [tex]\( B \)[/tex]
From the Total column 3:
[tex]\[ 60 + B = C \][/tex]
### Total Sum Equations:
We know that the sum of the Pie and Cake columns for all rows must equal the sum in the Total row:
[tex]\[
(Pie + Cake = Total)
\][/tex]
Summing all columns:
[tex]\[
(36 + 42 + 60) + (D + 7 + B) = (42 + A + C)
\][/tex]
As we have already calculated:
[tex]\[
138 + (6 + 7 + B) = 42 + 49 + C
\][/tex]
[tex]\[
138 + 13 + B = 91 + C
\][/tex]
### Step 4: Solve for [tex]\( B \)[/tex]
Given the variables should sum to match, equate the terms:
[tex]\[
151 + B = 91 + C
\][/tex]
[tex]\[
B = C - 60
\][/tex]
### Step 5: Selecting Correct [tex]\( C \)[/tex] from provided options
Testing the possible values for [tex]\( C \)[/tex]:
- If [tex]\( C = 66 \)[/tex]:
[tex]\[
B = 66 - 60 \implies B = 6
\][/tex]
[tex]\[
Check: \quad 60 + 6 = 66 \quad \rightarrow \text{Correct}
\][/tex]
Thus, [tex]\( \boxed{66} \)[/tex] is the correct solution and the value for [tex]\( C \)[/tex] is [tex]\( 66 \)[/tex].
