Final answer:
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.