Let's carefully analyze the given data and complete the two-way table.
Firstly, we can fill in some sections of the two-way table based on the provided information:
1. 122 people responded to the survey.
2. 68 people prefer splitting the check.
3. 56 people prefer to skip dessert.
4. 50 people who said they order dessert also prefer to split the check.
Next, let's add this information to our table:
\begin{tabular}{|c|c|c|}
\hline & order dessert & no dessert \\
\hline split the check & 50 & X \\
\hline one person pays & Y & Z \\
\hline
\end{tabular}
Here, [tex]\(X\)[/tex], [tex]\(Y\)[/tex], and [tex]\(Z\)[/tex] are unknown values we need to determine.
#### Step-by-step Analysis:
1. Calculate "split the check, no dessert" (X):
- We know 68 people prefer to split the check.
- Out of these 68 people, 50 people order dessert.
- Therefore, the number of people who prefer splitting the check but not ordering dessert is:
[tex]\[
X = 68 - 50 = 18
\][/tex]
2. Calculate total people who order dessert and who do not:
- Total people who skip dessert is given as 56.
- So, total people who order dessert is:
[tex]\[
122 - 56 = 66
\][/tex]
3. Calculate "one person pays, order dessert" (Y):
- We already know that 66 people order dessert.
- Out of these 66 people, 50 prefer to split the check.
- Thus, the number of people who order dessert and prefer one person to pay is:
[tex]\[
Y = 66 - 50 = 16
\][/tex]
4. Calculate "one person pays, no dessert" (Z):
- We know 56 people skip dessert.
- Out of these, 18 prefer to split the check.
- Thus, the number of people who skip dessert and prefer one person to pay is:
[tex]\[
Z = 56 - 18 = 38
\][/tex]
Now, let’s complete the table:
\begin{tabular}{|c|c|c|}
\hline & order dessert & no dessert \\
\hline split the check & 50 & 18 \\
\hline one person pays & 16 & 38 \\
\hline
\end{tabular}
### Final Answer:
The number of sampled adults who prefer to split the check but not order dessert is 18.
