Answer:
15x + 25y ≥ 400
x + 2y ≤ 20
x ≥ 0, y ≥ 0
Step-by-step explanation:
Here, we are modelling the total number of hours she can use in making images in a week and the total amount that can be earned in a week, considering the given constraints.
Number of small images in a week = x
Number of hrs in making images if it takes 1 hr to make 1 = 1*x = x
Number of large images in a week = y
Number of hrs in making large images if it takes 2 hrs to make 1 = 2*y = 2y
Given that she has up to 20 hrs to make the images, therefore, the inequality that models this situation would be:
x + 2y ≤ 20
This implies that, the hours spent altogether can be less than or equal to 20hrs
Amount for small images = $15
Amount in total for all images made in a week = $15*x = 15x
Amount for large images = $25
Amount in total for all images made in a week = $25*y = 25y
Given that she can earn AT LEAST $400 in a week, therefore, the inequality that models this situation would be:
15x + 25y ≥ 400
This implies that, the amount she wants to make in a week would be $400 or more.
The system of inequalities would be:
x + 2y ≤ 20
15x + 25y ≥ 400
x ≥ 0, y ≥ 0
