Question

Mary is planning to provide online math and french language tutoring sessions. The math session will be 45 minutes long, and the french sessions will be 30 minutes long. She plans to work no more than 30 hours per week and does not want to provide more than 30 french sessions in any one week l. Let m represent the number of math sessions, and f represent the number of french sessions mary will offer during the week. Which system of inequalities represents the constraints of the given situation?

Answer 1

3/4m + 1/2f ≤ 30

f ≤ 30

Explanation:

Answer 2

• 3/4m + 1/2f ≤ 30
• f ≤ 30

Explanation:

• Math session = 45 min = 3/4 hr
• French session = 30 min = 1/2 hr
• Number of math sessions = m, total math hours = 3/4m
• Number of French sessions = f, total French hours = 1/2f

Total hours constraint:

• 3/4m + 1/2f ≤ 30

Number of session constraint:

• f ≤ 30

So the system is:

• 3/4m + 1/2f ≤ 30
• f ≤ 30