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(−2,6)left parenthesis negative 2 comma 6 right parenthesis(2,4)left parenthesis 2 comma 4 right parenthesis(1,4.5)
Let x represent the number of hardback books and y represent the number of paperback books.
The total cost of hardbacks is 12x.
The total cost of paperbacks is 5y.
The inequality representing the budget constraint is:
12x + 5y ≤ 60
To check which of the given points represents a viable solution, substitute the values into the inequality:
1) (6,6):
12(6) + 5(6) = 72 + 30 = 102
This point does not satisfy the inequality.
2) (-2,6):
12(-2) + 5(6) = -24 + 30 = 6
This point satisfies the inequality.
3) (2,4):
12(2) + 5(4) = 24 + 20 = 44
This point satisfies the inequality.
4) (1,4.5):
12(1) + 5(4.5) = 12 + 22.5 = 34.5
This point satisfies the inequality.
Therefore, the viable solutions are (−2,6), (2,4), and (1,4.5).