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 (6,6) left parenthesis 6 comma 6 right parenthesis (2,4) left parenthesis 2 comma 4 right parenthesis (−2,6) left parenthesis negative 2 comma 6 right parenthesis (1,4.5)
Let h represent the number of hardbacks and p represent the number of paperbacks.
The cost of hardbacks is 12h.
The cost of paperbacks is 5p.
Since Kiani has a budget of $60, the total cost of the books cannot exceed $60.
Therefore, the two-variable inequality is:
12h + 5p ≤ 60
Now let's determine which point represents a viable solution by substituting the values into the inequality:
(6, 6): 12(6) + 5(6) = 72 + 30 = 102 (not a viable solution since it exceeds the budget)
(2, 4): 12(2) + 5(4) = 24 + 20 = 44 (a viable solution since it does not exceed the budget)
(-2, 6): 12(-2) + 5(6) = -24 + 30 = 6 (a viable solution since it does not exceed the budget)
(1, 4.5): 12(1) + 5(4.5) = 12 + 22.5 = 34.5 (a viable solution since it does not exceed the budget)
Therefore, the point that represents a viable solution is (2, 4).