An algebra teacher is writing a test. There will be two types of questions: multiple-choice and open-ended. The multiple-choice questions take 3 minutes to complete and the open-ended questions take 12 minutes to complete. There must be at least 3 open-ended questions, at least 10 multiple-choice questions, and the test should take no more than 84 minutes.
A: describe this scenario as a system of inequalities, use M for the number of multiple-choice questions and O for the number of open-ended questions.
M >= 10
O >= 3
3M+12O <= 84
Thank you so much.
To describe this scenario as a system of inequalities, we can use the following variables:
Let M be the number of multiple-choice questions, and O be the number of open-ended questions.
Given the conditions, we can write the following inequalities:
1. There must be at least 3 open-ended questions:
O ≥ 3
2. There must be at least 10 multiple-choice questions:
M ≥ 10
3. The time taken to complete multiple-choice questions (in minutes) is given by 3M, and open-ended questions take 12 minutes each. The total time should be no more than 84 minutes:
3M + 12O ≤ 84
Therefore, the system of inequalities that represents this scenario is:
O ≥ 3
M ≥ 10
3M + 12O ≤ 84