Antoine is on vacation with his family. They have a vacation budget of $1,400. Antoine predicts they will spend $110 each night on the hotel, $80 a day on food, and $100 a day on activities. They will also spend $120 on gasoline for the entire trip. Write an inequality to find how many nights, n, they afford to stay on vacation. What is the longest vacation they can take?

290n + 120 ≤ 1400

4 days

Step-by-step explanation:

Given that:

Vacation budget = $1400

Cost on hotel = $110 per night

Cost on food = $80 per day

Cost on activities = $100 per day

Cost on gas = $120 for entire trip

Number of nights they can afford to stay

Let the Number of nights they can afford = n

((110 + 80 + 100) * number of nights) + 120 ≤ vacation budget

290n + 120 ≤ 1400

290n ≤ 1400 - 120

290n ≤ 1280

n ≤ 1280 / 290

n ≤ 4.4137

Hence, longest vacation they can take is 4 days