Question

cate solved an inequality to find (c), the possible number of cats that a shelter can house. she found that (c < 28). which statement best describes a possible solution to cates problem?

• the shelter can house 28 cats because (28 < 28).
• the shelter can house 15.6 cats because (15.6 < 28).
• the shelter can house 17 cats because (17 < 28).
• the shelter can house (-8) cats because (-8 < 28).

Explanation:

Analyze the mathematical constraint

Using the Real-world Inequality Constraints knowledge point, we identify that the variable \(c\) represents the number of cats a shelter can house. The solved inequality is:

$$c < 28$$

Evaluate real-world context constraints

Using the Real-world Inequality Constraints knowledge point, we must apply physical constraints to the variable \(c\). Since \(c\) represents a count of living animals (cats), it must satisfy two real-world conditions:

1. It must be a non-negative value (\(c \ge 0\)).
2. It must be a whole number (an integer), as you cannot have a fraction of a cat.

Verify each option against constraints

Using the Solution Set Verification knowledge point, we test each given statement:

• Option 1: "The shelter can house 28 cats because \(28 < 28\)."

This is mathematically false because \(28\) is not strictly less than \(28\).

• Option 2: "The shelter can house 15.6 cats because \(15.6 < 28\)."

While mathematically true, a shelter cannot house a fractional number of cats (\(15.6\)).

• Option 3: "The shelter can house 17 cats because \(17 < 28\)."

This is mathematically true (\(17 < 28\)) and physically possible since \(17\) is a non-negative whole number.

• Option 4: "The shelter can house \(-8\) cats because \(-8 < 28\)."

While mathematically true, a shelter cannot house a negative number of cats (\(-8\)).

Select the best statement

Using the Solution Set Verification knowledge point, we conclude that housing 17 cats is the only mathematically valid and physically realistic solution.

Answer:

• (A) The shelter can house 28 cats because \(28 < 28\).
• (B) The shelter can house 15.6 cats because \(15.6 < 28\).
• (C) The shelter can house 17 cats because \(17 < 28\). (Correct answer)
• (D) The shelter can house \(-8\) cats because \(-8 < 28\).