Question

Antonina needs to have worked at least 909090 volunteer hours to graduate. She has already volunteered with a housing organization over the summer for 525252 hours. Antonina needs to tutor after school for 333 hours per week to complete the remainder of her volunteer hours. If www 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

An inequality can be formed by simply translating the problem statement to numerical expressions.

From the problem we know that $3w$ added with $52$ hours should be equal or greater than $90$ (helpful insight from the keyword "at least"). Therefore, it's inequality would look like:

$3w+52>=90$ (>= is used instead of ≥ for constraints in formatting)

The inequality above best models the situation.

Answer 2

Answer: 13 weeks.

Step-by-step explanation:

Every number seems to be tripled:

we have that:

Antonia needs to have worked at least 90 volunteer hours.

She already has worked 52 hours over the summer

She needs to work 3 hours per week to complete her remainder, we want to find how many weeks she needs to work.

the hours that she needs to work are:

90 - 52 = 38

she needs to work 38 hours, then, at a rate of 3 hours per week we have that:

w = 38/3 = 12.67

but we need to round up this, so we would have 13 weeks.

and she will work a total of 3*13 = 39 hours, plus the 52 that she already had this ad to 91 hours, so she will complete the minimum of 90 hours.