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Northlake High School has two lunch periods. Students can eat their lunch in the cafeteria or on an outside patio. About [tex]$31 \%$[/tex] of students who have first lunch eat outside. Compare this with the percentage of second-lunch students who eat outside.

\begin{tabular}{|c|c|c|c|}
\hline & Eat outside & Eat inside & Total \\
\hline First lunch & 0.17 & 0.38 & 0.55 \\
\hline Second lunch & 0.21 & 0.24 & 0.45 \\
\hline Total & 0.38 & 0.62 & 1.0 \\
\hline
\end{tabular}

Select the true statement.

A. A higher percentage of students eat outside during the second lunch compared to the first lunch.
B. A higher percentage of students eat inside during the second lunch compared to the first lunch.
C. An equal percentage of students eat outside during both lunch periods.
D. More students eat inside during the first lunch compared to the second lunch.



Answer :

GinnyAnswer
To determine the true statement regarding the percentages of students eating outside during the first and second lunch periods, we will calculate the percentage of students eating outside for both periods and compare them to the provided percentage of 31%. Here are the steps:

1. Calculate the percentage of first-lunch students who eat outside:
- The number of first-lunch students who eat outside is given as 0.17 (17%).
- The total number of first-lunch students is given as 0.55 (55%).
- Calculate the percentage of first-lunch students who eat outside:
[tex]\[ \text{Percentage of first-lunch students who eat outside} = \left( \frac{0.17}{0.55} \right) \times 100 \][/tex]
- Substituting the values in, we get:
[tex]\[ \frac{0.17}{0.55} \approx 0.3090 \quad \text{(or 30.909%)} \][/tex]

2. Calculate the percentage of second-lunch students who eat outside:
- The number of second-lunch students who eat outside is given as 0.21 (21%).
- The total number of second-lunch students is given as 0.45 (45%).
- Calculate the percentage of second-lunch students who eat outside:
[tex]\[ \text{Percentage of second-lunch students who eat outside} = \left( \frac{0.21}{0.45} \right) \times 100 \][/tex]
- Substituting the values in, we get:
[tex]\[ \frac{0.21}{0.45} \approx 0.4667 \quad \text{(or 46.667%)} \][/tex]

3. Compare these percentages with the provided 31% and determine the true statement:
- The percentage of first-lunch students who eat outside is approximately 30.909%, which is less than 31%.
- The percentage of second-lunch students who eat outside is approximately 46.667%.

Based on these calculations, we can conclude the true statement is:
- The percentage of second-lunch students who eat outside (46.667%) is greater than the mentioned 31%. The percentage of first-lunch students who eat outside (30.909%) is just below 31%, confirming it and indicating the second-lunch period has a higher percentage of students eating outside.

To summarize, the true statement is:
- "Less than 31% of the students who have first lunch eat outside, whereas 46.667% of second-lunch students eat outside."

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