Kiani is shopping at a bookstore with a budget of $60 hard backs cost $12 and paperbacks cost $5 Ray two variable inequality and determine the constraints of the problem which of the following points represents a variable solution is it negative 2, 6 One, 4.5 6, 6 or 2, 4
Let's represent the number of hardbacks as "x" and the number of paperbacks as "y".
From the given information, we know that Kiani's budget is $60, which can be expressed as the inequality:
12x + 5y ≤ 60
Additionally, we have the constraint that Kiani cannot purchase a negative number of books, so x ≥ 0 and y ≥ 0.
Now, let's plug in the coordinate points given and see if they satisfy the inequalities:
1) (−2, 6):
12(-2) + 5(6) = -24 + 30 = 6 ≤ 60 ----> This point satisfies the inequality.
2) (4.5, 6):
12(4.5) + 5(6) = 54 + 30 = 84 > 60 ----> This point does NOT satisfy the inequality.
3) (6, 6):
12(6) + 5(6) = 72 + 30 = 102 > 60 ----> This point does NOT satisfy the inequality.
4) (2, 4):
12(2) + 5(4) = 24 + 20 = 44 ≤ 60 ----> This point satisfies the inequality.
Therefore, the variable solution that represents the point satisfying the given constraints is (−2, 6).