To determine how much Annie can spend on lunch for each person while staying within her budget, let's break down the problem with the given information.
1. Annie's total budget is [tex]\(\$ 1325\)[/tex].
2. She plans to rent a meeting room, which costs [tex]\(\$ 270\)[/tex].
3. 26 people (including Annie) are expected to attend the meeting.
4. We need to find the maximum amount [tex]\( x \)[/tex] that Annie can spend on lunch for each person.
Step-by-Step Solution:
1. Total budget constraint:
The entire expenditure (room cost plus lunch cost) must not exceed the budget.
2. Cost of the meeting room:
The meeting room costs [tex]\(\$ 270\)[/tex], so this amount is reserved from the total budget.
3. Cost of lunch per person:
Let [tex]\( x \)[/tex] be the amount Annie can spend on lunch for each person. Since there are 26 people, the total cost for lunch is [tex]\( 26x \)[/tex].
4. Setting up the inequality:
The sum of the room cost and the total lunch cost should be at most the total budget:
[tex]\[
270 + 26x \leq 1325
\][/tex]
This inequality reflects that the combined cost should not exceed the total budget.
Now, let's review the options:
A. [tex]\( 26x + 270 \geq 1325 \)[/tex] => This inequality suggests that the combined cost must be greater than or equal to the budget, which is incorrect for our situation.
B. [tex]\( 26x + 270 \leq 1325 \)[/tex] => This inequality correctly represents that the combined cost should not exceed the total budget.
C. [tex]\( 270x + 26 \geq 1325 \)[/tex] => This inequality incorrectly places the room cost as a multiple of [tex]\(x\)[/tex], which is not correct.
D. [tex]\( 270x + 26 \leq 1325 \)[/tex] => This inequality also incorrectly places the room cost as a multiple of [tex]\(x\)[/tex], which is not correct.
From the options given, the correct inequality is:
[tex]\[
\boxed{26x + 270 \leq 1325}
\][/tex]
Thus, the correct answer is:
B. [tex]\( 26x + 270 \leq 1325 \)[/tex]
