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?
• (1,4.5)
• (-2,6)
• (2,4)
• (6,6)
Let x be the number of hardbacks Kiani buys and y be the number of paperbacks Kiani buys.
The inequality can be written as: 12x + 5y ≤ 60
The constraints of the problem are:
x ≥ 0 (The number of hardbacks cannot be negative)
y ≥ 0 (The number of paperbacks cannot be negative)
12x + 5y ≤ 60 (The total cost of the books cannot exceed the budget of $60)
To determine which of the following points represents a viable solution, substitute the values into the inequality:
(1,4.5):
12(1) + 5(4.5) = 12 + 22.5 = 34.5 which is less than or equal to 60. This point is a viable solution.
(-2,6):
12(-2) + 5(6) = -24 + 30 = 6 which is less than or equal to 60. This point is a viable solution.
(2,4):
12(2) + 5(4) = 24 + 20 = 44 which is less than or equal to 60. This point is a viable solution.
(6,6):
12(6) + 5(6) = 72 + 30 = 102 which is greater than 60. This point is not a viable solution.
Therefore, the viable solutions are (1,4.5), (-2,6), and (2,4).