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

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.

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.

Answer 2

Let's denote the number of servings of dry food as "x" and the number of servings of wet food as "y".

The cost of x servings of dry food is $1 * x = $1x.
The cost of y servings of wet food is $3 * y = $3y.

We need to set up the following inequalities to represent the scenario:

1) The total number of servings should be at least 2: x + y ≥ 2
2) The total cost should be less than or equal to $9: $1x + $3y ≤ $9

So, the system of inequalities that models this scenario is:

x + y ≥ 2
$1x + $3y ≤ $9