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
(−2,6)
left parenthesis negative 2 comma 6 right parenthesis
(2,4)
left parenthesis 2 comma 4 right parenthesis
(6,6)
left parenthesis 6 comma 6 right parenthesis
(1,4.5)
Let x represent the number of hardbacks and y represent the number of paperbacks. The cost of the hardbacks is 12x and the cost of the paperbacks is 5y. The inequality representing the budget constraint is:
12x + 5y ≤ 60
Now we can test each option to see if it satisfies the inequality:
(−2,6):
12(-2) + 5(6) = -24 + 30 = 6
6 ≤ 60
This point is a viable solution.
(2,4):
12(2) + 5(4) = 24 + 20 = 44
44 ≤ 60
This point is a viable solution.
(6,6):
12(6) + 5(6) = 72 + 30 = 102
102 ≤ 60
This point is NOT a viable solution.
(1,4.5):
12(1) + 5(4.5) = 12 + 22.5 = 34.5
34.5 ≤ 60
This point is a viable solution.
Therefore, the viable solution is (−2,6) or, in coordinate form, (-2, 6).