Final answer:
Briyana needs to save for at least 10 weeks to reach her goal of saving at least $560 for her spring break trip, starting with her current savings of $150 and saving $45 per week.
Step-by-step explanation:
To determine how long it will take Briyana to save at least $560 for a spring break trip with her current savings of $150 and the ability to save $45 per week, we can set up an inequality. The inequality will represent the total amount Briyana will save over w weeks. We start with her current savings, $150, and add to that the product of $45 and the number of weeks she saves, which is represented by w. Thus, the inequality is:
45w + 150 ≥ 560
This inequality states that the amount saved over w weeks, when added to her initial savings, must be at least $560. To solve for w, we can subtract 150 from both sides of the inequality, then divide by 45:
(45w + 150) - 150 ≥ 560 - 150
45w ≥ 410
Dividing both sides by 45:
w ≥ 410 / 45
Calculating the division:
w ≥ 9.11
Since Briyana cannot save for a fraction of a week, she must save for at least 10 full weeks to ensure she has enough for her trip.