Final answer:
The correct system of inequalities to represent Rody's summer job conditions is 'x + y ≤ 13 and 10x + 15y ≥ 150'. Graphing these yields a solution such as 'x = 5, y = 8', where Rody works 5 hours babysitting and 8 hours clearing tables, satisfying both the hour and income requirements. The correct option is C.
Step-by-step explanation:
The student asks to write and solve a system of inequalities graphically and determine one possible solution to meet Rody's work and income conditions for his summer jobs.
The correct system of inequalities representing Rody's situation is c) x + y ≤ 13 and 10x + 15y ≥ 150. This means that the number of hours spent babysitting (x) and clearing tables (y) must be less than or equal to 13, and the total earnings from both jobs must be at least $150.
To find one possible solution, we must graph these inequalities on the coordinate plane, looking for the region where both conditions are satisfied. Here are the steps to graphing the inequalities:
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- Graph the line x + y = 13 by plotting the points where x = 0, y = 13 and x = 13, y = 0, and then draw a line through these points. As we're looking for x + y ≤ 13, shade the area below this line.
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- Graph the line 10x + 15y = 150 by plotting the intercepts x = 0, y = 10 and x = 15, y = 0, and then draw a line through these points. The inequality 10x + 15y ≥ 150 means we shade the area above this line.
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- The solution region is where the shaded areas of both inequalities overlap.
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- Choose any point within the overlapping shaded region as a possible solution. For example, x = 5, y = 8 is a solution because it satisfies both inequalities: 5 + 8 ≤ 13 and 10(5) + 15(8) ≥ 150.
Therefore, the correct option with a possible solution is c) x + y ≤ 13 and 10x + 15y ≥ 150; Solution: x = 5, y = 8.