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)

(2,4)

(-2,6)

(1,4.5)

(6,6)

Answer 1

Let x = number of hardbacks and y = number of paperbacks. The cost constraint is
12x + 5y ≤ 60.
Also x ≥ 0, y ≥ 0 and x,y must be whole numbers (integers).

Test the points:
- (2,4): 12(2)+5(4)=24+20=44 ≤60 — viable.
- (-2,6): x < 0 — not allowed.
- (1,4.5): y is not an integer (fractional books) — not allowed.
- (6,6): 12(6)+5(6)=72+30=102 >60 — over budget.

Thus (2,4) is the only viable solution.