To create a two-variable inequality based on Kiani's shopping scenario, we can let:
- \( x \) represent the number of hardbacks purchased.
- \( y \) represent the number of paperbacks purchased.
The total cost of the hardbacks and paperbacks must not exceed Kiani's budget of $60. Thus, we can write the inequality as:
\[ 12x + 5y \leq 60 \]
Next, we need to consider the constraints of the problem:
- Non-negativity constraint: Kiani cannot buy a negative number of books. Therefore:
- \( x \geq 0 \)
- \( y \geq 0 \)
Combining these constraints, we have the system:
- \( 12x + 5y \leq 60 \)
- \( x \geq 0 \)
- \( y \geq 0 \)
Now let's evaluate the given points to see which represents a viable solution:
A: \( (1, 4.5) \)
\[ 12(1) + 5(4.5) = 12 + 22.5 = 34.5 \leq 60 \quad \text{(valid)} \]
B: \( (2, 4) \)
\[ 12(2) + 5(4) = 24 + 20 = 44 \leq 60 \quad \text{(valid)} \]
C: \( (6, 6) \)
\[ 12(6) + 5(6) = 72 + 30 = 102 \leq 60 \quad \text{(invalid)} \]
D: \( (-2, 6) \)
\[ \text{(not valid since x cannot be negative)} \]
Based on the evaluations, the viable solutions are:
- A: (1, 4.5) is valid.
- B: (2, 4) is valid.
C and D are not valid solutions.
Thus, both A and B are viable points that satisfy the constraints and the inequality. If we need to choose only one viable solution from the options, we can select either A or B.