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Answer :
Sure! Let's break down the problem step-by-step to determine how many nights Sammy can stay in Nashville within his budget.
1. Understand the costs involved:
- The hotel cost is [tex]$125 per night.
- The round-trip flight costs $[/tex]159.
2. Total available budget:
- Sammy has a total of [tex]$900 to spend on his trip.
3. Setting up the inequality:
- Let \( n \) be the number of nights Sammy stays in the hotel.
- The total cost for \( n \) nights at the hotel is \( 125n \).
- The total cost for the trip, including the flight, is therefore \( 125n + 159 \).
4. Making sure the total cost does not exceed the budget:
- Sammy's total cost needs to be less than or equal to his budget of $[/tex]900.
- So, we set up the inequality: [tex]\( 125n + 159 \leq 900 \)[/tex].
5. Selecting the correct inequality:
- The inequality [tex]\( 125n + 159 \leq 900 \)[/tex] correctly represents Sammy's budget to find out how many nights he can stay in Nashville.
Given the options:
a) [tex]\( 125n + 159 \geq 900 \)[/tex] - This suggests the costs should be greater than or equal to [tex]$900, which is incorrect.
b) \( 125n + 159 \leq 900 \) - This correctly states that the total cost should not exceed $[/tex]900. This is the correct inequality.
c) [tex]\( 159n + 125 \leq 900 \)[/tex] - This incorrectly places the flight cost per night, which is not correct.
d) [tex]\( 159\pi + 125 \geq 900 \)[/tex] - This option does not make sense since [tex]\(\pi\)[/tex] is unrelated to the problem.
Thus, the correct answer is:
b) [tex]\( 125n + 159 \leq 900 \)[/tex]
1. Understand the costs involved:
- The hotel cost is [tex]$125 per night.
- The round-trip flight costs $[/tex]159.
2. Total available budget:
- Sammy has a total of [tex]$900 to spend on his trip.
3. Setting up the inequality:
- Let \( n \) be the number of nights Sammy stays in the hotel.
- The total cost for \( n \) nights at the hotel is \( 125n \).
- The total cost for the trip, including the flight, is therefore \( 125n + 159 \).
4. Making sure the total cost does not exceed the budget:
- Sammy's total cost needs to be less than or equal to his budget of $[/tex]900.
- So, we set up the inequality: [tex]\( 125n + 159 \leq 900 \)[/tex].
5. Selecting the correct inequality:
- The inequality [tex]\( 125n + 159 \leq 900 \)[/tex] correctly represents Sammy's budget to find out how many nights he can stay in Nashville.
Given the options:
a) [tex]\( 125n + 159 \geq 900 \)[/tex] - This suggests the costs should be greater than or equal to [tex]$900, which is incorrect.
b) \( 125n + 159 \leq 900 \) - This correctly states that the total cost should not exceed $[/tex]900. This is the correct inequality.
c) [tex]\( 159n + 125 \leq 900 \)[/tex] - This incorrectly places the flight cost per night, which is not correct.
d) [tex]\( 159\pi + 125 \geq 900 \)[/tex] - This option does not make sense since [tex]\(\pi\)[/tex] is unrelated to the problem.
Thus, the correct answer is:
b) [tex]\( 125n + 159 \leq 900 \)[/tex]
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