Question

Question Kiani is shopping at a bookstore with a budget of $60. Hardbacks cost $12 and paperbacks cost $5. Write a two-variable inequality and determine the constraints of the problem. Which of the following points represents a viable solution?(1 point) Responses (2,4) left parenthesis 2 comma 4 right parenthesis (1,4.5) left parenthesis 1 comma 4.5 right parenthesis (6,6) left parenthesis 6 comma 6 right parenthesis (−2,6)

Answer 1

To model Kiani's shopping situation, we can denote the number of hardbacks bought as \( x \) and the number of paperbacks bought as \( y \). Given the prices of the books and Kiani's budget, we can establish the following inequality:

\[ 12x + 5y \leq 60 \]

### Constraints of the Problem:
1. **Non-negativity**: Kiani cannot buy a negative number of books, so:
\[
x \geq 0 \quad \text{and} \quad y \geq 0
\]

### Now we will check which of the provided points is a viable solution:

1. **Point (2, 4)**:
\[
12(2) + 5(4) = 24 + 20 = 44 \leq 60 \quad \text{(Valid)}
\]

2. **Point (1, 4.5)**:
\[
12(1) + 5(4.5) = 12 + 22.5 = 34.5 \leq 60 \quad \text{(Valid)}
\]

3. **Point (6, 6)**:
\[
12(6) + 5(6) = 72 + 30 = 102 \not\leq 60 \quad \text{(Invalid)}
\]

4. **Point (-2, 6)**:
\[
\text{(Invalid because } x \text{ must be non-negative)}
\]

### Conclusion:
The viable solutions from the given options are (2, 4) and (1, 4.5).

Hence, the points that represent viable solutions are (2, 4) and (1, 4.5).