Question

Antonina needs to have worked at least 90 volunteer hours to graduate. She has already volunteered with a housing organization over the summer for 52 hours. Antonina needs to tutor after school for 3 hours per week to complete the remainder of her volunteer hours. If w is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours, which of the following inequalities best models the situation described above?

Answer 1

No. of hours already volunteered + total volunteer hours dedicated in w weeks > = Least volunteer hours required to graduate

=> 52 + 3w >= 90

Explanation:

Given that Antonina needs to have worked at least 90 volunteer hours to graduate means that she needs to volunteer either for 90 hours or more than that . Mathematically this can be written as

Total volunteer hours required to graduate greater than or equal to 90

Total volunteer hours required to graduate>= 90

No. of hours already volunteered = 52

no. of hours left for volunteering = Total volunteer hours required to graduate - No. of hours already volunteered = 90 - 52 = 38

No. of hours in one week she can dedicate for volunteering= 3

if w is the number of weeks that Antonina needs to tutor in order to complete her volunteer hours

then total volunteer hours dedicated in w weeks will be = w*No. of hours in one week she can dedicate for volunteering = w*3 = 3w

Thus,

No. of hours already volunteered + total volunteer hours dedicated in w weeks > = Least volunteer hours required to graduate

=> 52 + 3w >= 90