Question

Which linear inequality correctly models the situation where you need to complete at least 10 geometry problems and at least 10 algebra problems within 2 hours, with each geometry problem taking 30 minutes and each algebra problem taking 10 minutes?

Option 1: 30g + 10a ≤ 120
Option 2: 30g + 10a ≥ 120
Option 3: 30g + 10a < 120
Option 4: 30g + 10a > 120

Answer 1

Option 2: 30g + 10a ≥ 120 is the correct linear inequality that models the situation.

Step-by-step explanation:

The correct linear inequality that models the situation is Option 2: 30g + 10a ≥ 120.

• g represents the number of geometry problems
• a represents the number of algebra problems
• The inequality ≥ (greater than or equal to) indicates that the total time should be greater than or equal to 120 minutes.

Using this inequality, we can calculate the total time for both types of problems. Since each geometry problem takes 30 minutes and each algebra problem takes 10 minutes, the inequality becomes 30g + 10a ≥ 120.