Michelle has $9 and wants to buy a combination of dog food to feed at least two dogs at the animal shelter. A serving of dry food costs $1, and a serving of wet food costs $3.

Question

Part A: Write the system of inequalities that models this scenario

Answer 1

Let x be the number of servings of dry food, and y be the number of servings of wet food. Michelle wants to feed at least 2 dogs, so we can write the inequality:

x + y ≥ 2

The cost of x servings of dry food and y servings of wet food is:

C = 1x + 3y

Michelle has $9 to spend, so we can write the inequality:

C ≤ 9

Putting it all together, the system of inequalities that models this scenario is:

x + y ≥ 2
1x + 3y ≤ 9

Note: We don't need to add additional constraints for the non-negativity of x and y because we can't have negative servings of dog food in this case.