Kiani is shopping at a bookstore with a budget of $60. Hardback cost $12 and paperbacks cost $5. Write a two-variable inequality and dertermine the costraints of the problem. Which of the following points represents a viable solution?
A. (6, 6)
B. (1, 4.5)
C. (2, 4)
D. (-2, 6)
Let x be the number of hardback books and y be the number of paperbacks books purchased.
The cost constraint can be represented by the inequality: 12x + 5y ≤ 60
The constraints of the problem are:
- x and y must both be non-negative (x, y ≥ 0)
- x and y must be integers
To determine the viable solution, substitute each point into the inequality and check if it satisfies the constraints:
A. (6, 6): 12(6) + 5(6) = 72 + 30 = 102, which is greater than 60. Not a viable solution.
B. (1, 4.5): 12(1) + 5(4.5) = 12 + 22.5 = 34.5, which is less than 60. Viable solution.
C. (2, 4): 12(2) + 5(4) = 24 + 20 = 44, which is less than 60. Viable solution.
D. (-2, 6): 12(-2) + 5(6) = -24 + 30 = 6, which is less than 60. However, this point violates the constraint x ≥ 0. Not a viable solution.
Therefore, the viable solutions are B. (1, 4.5) and C. (2, 4).