Answer:
Option A: Elena can work as a server for 5 hours and edit poetry for 10 hours.
Step-by-step 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.