Question

Jorelle is planning a 5-day vacation. The trip will cost him $1,300.00 for airfare, food, and itineraries. He plans to stay in a hotel room for $80.00 per night. He only has $950.00 in savings, but he earns $25.00 per hour from his online tutoring services. Create a linear inequality in one variable that would best translate the problem. Determine the minimum number of hours Jorelle must tutor so he can have enough money for the trip

Answer 1

To set up a linear inequality to represent Jorelle's situation, let's define the variable:

• Let \( x \) represent the number of hours Jorelle will tutor.

Costs Breakdown

1. The total cost of the trip is $1,300.00.
2. The hotel room costs $80.00 per night for 5 nights: \[ \text{Cost of hotel} = 5 \times 80 = 400 \]
3. The remaining expenses (airfare, food, and itineraries) is: \[ \text{Other costs} = 1300 - 400 = 900 \]

Funds Available

1. Jorelle has $950.00 in savings.
2. He earns $25.00 per hour, so after working \( x \) hours, he will earn: \[ \text{Earnings from tutoring} = 25x \]

Total Money Available

The total amount of money Jorelle will have (savings plus tutoring earnings) is: \[ \text{Total money} = 950 + 25x \]

Inequality

To ensure he has enough money for the trip, we need the total money he will have to be at least $1,300: \[ 950 + 25x \geq 1300 \]

Solve the Inequality

Now, let's solve for \( x \):

1. Subtract 950 from both sides: \[ 25x \geq 1300 - 950 \] \[ 25x \geq 350 \]
2. Divide both sides by 25: \[ x \geq \frac{350}{25} \] \[ x \geq 14 \]

Conclusion

Jorelle must tutor at least 14 hours in order to have enough money for his trip. The linear inequality that represents this situation is: \[ 950 + 25x \geq 1300 \]