Savannah sells character images online. Small images take one hour to make and she sells them for $15. Large images sell for $25 and take two hours to make. Each week, Savannah can work up to 20 hours making images, and she wants to earn at least $400. Let x represent the number of small images Savannah makes in a week, and let y represent the number of large images. Which of the following systems of inequalities models the constraints of this situation?

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