Final answer:
The correct linear inequality to represent the situation is 8x + 16y ≥ 208. This equation allows us to calculate various combinations of hours spent house cleaning (x) and at a sales job (y) that will yield at least $208 to cover the weekly bills. Example calculations can be represented in a table form to show different possible combinations of work hours that meet the budget requirement.
Step-by-step explanation:
To determine the number of hours you can spend house cleaning (x) and at your sales job (y) if you want to pay your bills, we use the given linear inequality: 8x + 16y ≥ 208. This inequality represents the minimum weekly earnings needed to pay bills. To create a table, we can choose various numbers of hours for house cleaning (x) and calculate the corresponding hours at the sales job (y) using the inequality. Here's an example table:
- House Cleaning Hours (x): 0, Sales Job Hours (y): 13 (since 16y = 208)
- House Cleaning Hours (x): 10, Sales Job Hours (y): 10 (since 8(10) + 16(10) = 240)
- House Cleaning Hours (x): 26, Sales Job Hours (y): 0 (since 8(26) = 208)
Note that this satisfies the inequality because, as long as the sum of 8 times the hours spent house cleaning and 16 times the hours at the sales job is at least 208, the bills will be paid. These pairs of values (x and y) are points that will lie on or above the line when plotted on a graph, representing all possible combinations of hours that will allow for at least $208 to be earned.