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Annie is planning a business meeting for her company. She has a budget of [tex]\$1,325[/tex] for renting a meeting room at a local hotel and providing lunch. She expects 26 people to attend the meeting. The cost of renting the meeting room is [tex]\$270[/tex]. Which inequality shows the amount, [tex]x[/tex], Annie can spend on lunch for each person?

A. [tex]26x + 270 \geq 1,325[/tex]
B. [tex]26x + 270 \leq 1,325[/tex]
C. [tex]270x + 26 \geq 1,325[/tex]
D. [tex]270x + 26 \leq 1,325[/tex]



Answer :

GinnyAnswer
Okay, let's break down this problem step-by-step to determine the correct inequality.

1. Identify the total budget and expenses:
- Annie's total budget is \[tex]$1,325. - The cost of renting the meeting room is \$[/tex]270.
- Annie expects 26 people to attend the meeting.
- We want to find out the maximum amount Annie can spend on lunch per person, denoted as [tex]\( x \)[/tex].

2. Set up the total cost equation:
The total cost will include:
- The cost of the meeting room.
- The cost of lunch for 26 people.

3. Expression for the total cost:
- The total cost for lunch for all 26 people will be [tex]\( 26x \)[/tex].
- Adding the cost of the room rental, the total cost equation will be:
[tex]\[ 26x + 270 \][/tex]

4. Inequality for the budget constraint:
Annie's budget should cover the total cost, so the inequality that represents this situation is:
[tex]\[ 26x + 270 \leq 1325 \][/tex]

5. Verifying the correct inequality:
Based on the correct mathematical setup for the problem, the appropriate inequality to determine the amount [tex]\( x \)[/tex] Annie can spend on lunch per person is:
[tex]\[ \boxed{26x + 270 \leq 1325} \][/tex]

So, the correct option is:
B. [tex]\( 26x + 270 \leq 1325 \)[/tex]