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)

Question

A: (1,4.5)
B: (2,4)
C: (6,6)
D: (−2,6)

Answer 1

To represent the number of hardbacks (let's call this \( x \)) and the number of paperbacks (let's call this \( y \)), we can formulate the following inequality based on Kiani's budget of $60:

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

Constraints of the Problem

1. Non-negativity constraints:

   • Since Kiani cannot buy a negative number of books, we have: \[ x \geq 0 \] \[ y \geq 0 \]

2. Budget constraint:

   • The combined cost of the hardbacks and paperbacks should not exceed $60: \[ 12x + 5y \leq 60 \]

Evaluating the Given Points

Now, let's evaluate each of the answer options to determine if they represent viable solutions.

• Point A: (1, 4.5) \[ 12(1) + 5(4.5) = 12 + 22.5 = 34.5 \text{ (which is } \leq 60) \]

• Point B: (2, 4) \[ 12(2) + 5(4) = 24 + 20 = 44 \text{ (which is } \leq 60) \]

• Point C: (6, 6) \[ 12(6) + 5(6) = 72 + 30 = 102 \text{ (which is } > 60) \]

• Point D: (−2, 6)

  • Since this point has a negative value for \( x \), it does not meet the non-negativity constraint.

Viable Solutions

From the evaluations, points A and B represent viable solutions.

However, if we need to choose only one from the provided options based on the question asking for a single viable point, then:

Answer: (2, 4) (Option B) is a viable solution that adheres to both constraints.