Question

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

(1,4.5)
(1,4.5)

(6,6)
(6,6)

(-2,6)
(-2,6)

(2,4)

Answer 1

Let x = number of hardbacks and y = number of paperbacks. The budget gives the inequality
12x + 5y ≤ 60.
Constraints: x ≥ 0, y ≥ 0 and x,y must be integers (you can’t buy fractional books).

Test the choices:
- (1,4.5): satisfies the money inequality but y is not an integer → not allowed.
- (6,6): 12(6)+5(6)=102 > 60 → over budget.
- (-2,6): x is negative → not allowed.
- (2,4): 12(2)+5(4)=44 ≤ 60 and both nonnegative integers → viable.

So (2,4) is the viable solution.