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
(2,4)
left parenthesis 2 comma 4 right parenthesis
(−2,6)
left parenthesis negative 2 comma 6 right parenthesis
(6,6)
left parenthesis 6 comma 6 right parenthesis
(1,4.5)
left parenthesis 1 comma 4.5 right parenthesis
Let x represent the number of hardback books purchased and y represent the number of paperback books purchased. The total cost can be represented by the inequality:
12x + 5y ≤ 60
The constraints are:
1. x ≥ 0 (non-negative number of hardback books)
2. y ≥ 0 (non-negative number of paperback books)
To determine which of the following points represents a viable solution, we can substitute each point into the inequality:
1. (2,4):
12(2) + 5(4) = 24 + 20 = 44 ≤ 60 (valid)
2. (-2,6):
12(-2) + 5(6) = -24 + 30 = 6 ≤ 60 (valid)
3. (6,6):
12(6) + 5(6) = 72 + 30 = 102 > 60 (invalid)
4. (1,4.5):
12(1) + 5(4.5) = 12 + 22.5 = 34.5 ≤ 60 (valid)
Therefore, the viable solutions are (2,4), (-2,6), and (1,4.5).