Question

Elena earns $10.50 per hour as a server working x hours per week. She also earns $8.50 per hour editing poetry for y hours per week. Elena needs to make at least $125 to pay her cell phone bill, but she has at most 17 total hours to work per week with her busy college schedule. The system of linear inequalities modeling this situation is shown. 10.50x+8.50y≥125 x+y≤17 Which statement represents a solution to the system of linear inequalities? Elena can work as a server for 5 hours and edit poetry for 10 hours. Elena can work as a server for 5 hours and edit poetry for 10 hours. Elena can work as a server for 10 hours and edit poetry for 9 hours. Elena can work as a server for 10 hours and edit poetry for 9 hours. Elena can work as a server for 10 hours and edit poetry for 1 hour. Elena can work as a server for 10 hours and edit poetry for 1 hour. Elena can work as a server for 3 hours and edit poetry for 10 hours.

Answer 1

Answer:

Option A: Elena can work as a server for 5 hours and edit poetry for 10 hours.

Explanation:

We are given the system of linear inequalities modeling this situation as; 10.50x + 8.50y ≥ 125

x + y ≤ 17

Where;

x represents number of server working hours per week.

y represents number of editing poetry hours per week.

In option A, x = 5 and y = 10. Let's plug them both into the first equation;

10.50(5) + 8.50(10) ≥ 125

Left hand side gives 137.5. So it fulfills the inequality.

Repeating the same for the 2nd equation, we have;

5 + 10 ≤ 17

Left hand side is 15 and it fulfills the equation. Option A is correct.

In option B, x = 10 and y = 9. Let's plug them both into the first equation;

10.50(10) + 8.50(9) ≥ 125

Left hand side gives 181.5. So it fulfills the inequality.

Repeating the same for the 2nd equation, we have;

10 + 9 ≤ 17

Left hand side is 17 and it doesn't fulfill the inequality. Option B is wrong.

In option C, x = 10 and y = 1. Let's plug them both into the first equation;

10.50(10) + 8.50(1) ≥ 125

Left hand side gives 113.5. So it doesn't fulfill the inequality.

Option C is wrong.

In option D, x = 3 and y = 10. Let's plug them both into the first equation;

10.50(3) + 8.50(10) ≥ 125

Left hand side gives 116.5. So it doesn't fulfill the inequality.

Option D is wrong.