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?

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

=> 52 + 3w >= 90

Step-by-step 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

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

it is 10.6 according to my calculations