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)

(6,6)


(2,4)


(1,4.5)


(−2,6)

Answer 1

Let h = number of hardbacks and p = number of paperbacks. The budget inequality is
12h + 5p ≤ 60.
Constraints: h ≥ 0, p ≥ 0 and h, p must be whole numbers (you can’t buy a negative or fractional book).

Check the points:
- (6,6): 12·6 + 5·6 = 102 > 60 → not viable.
- (2,4): 12·2 + 5·4 = 44 ≤ 60 → viable.
- (1,4.5): 12·1 + 5·4.5 = 34.5 ≤ 60 but p = 4.5 is not allowed → not viable.
- (−2,6): h = −2 is not allowed → not viable.

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