Question

Jude's family is planning a road trip. They are planning a budget and have $600 to spend on accommodations. They know that campsites cost $20 per night and hotel rooms cost $140 per night.

A. Write a linear inequality to describe this situation. Let x represent the number of nights that Jude's family camps and let y represent the number of nights that Jude's family stays in a hotel.

Answer 1

Jude's family's road trip budget can be described with the linear inequality 20x + 140y ≤ 600, where x is the number of camping nights and y is the number of hotel nights. The inequality represents the total accommodation cost not to exceed $600. They can stay a maximum of 2 nights in a hotel if they camp for 10 nights.

Step-by-step explanation:

Jude's family is budgeting for a road trip and has $600 to spend on accommodations. To describe this situation with a linear inequality where x represents the number of nights camping and y represents the number of nights in a hotel, we start by writing an equation that reflects the total cost of both choices not exceeding the budget of $600. The equation for the cost of camping is $20 per night, and the cost for a hotel room is $140 per night.

The linear inequality that represents this situation is:

20x + 140y ≤ 600

To solve the mathematical problem completely, Jude's family can plug in different values for x and y to see the combination of nights camping and staying in a hotel that will keep them at or under budget. For example, if they choose to camp for 10 nights (x = 10), they could calculate how many nights they could afford to stay in a hotel by rearranging the inequality to solve for y:

20(10) + 140y ≤ 600
200 + 140y ≤ 600
140y ≤ 400
y ≤ 2.857

Since they cannot stay in a hotel for a fraction of a night, the maximum number of hotel nights is 2 when they camp for 10 nights.