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)

(1,4.5)

(6,6)

(-2,6)

(2,4)

Answer 1

Let h = number of hardbacks and p = number of paperbacks. The budget gives the inequality
12h + 5p ≤ 60.
Also h ≥ 0, p ≥ 0 and (since books are whole) h and p are integers.

Check the points:
- (1, 4.5): 12(1)+5(4.5)=12+22.5=34.5 ≤ 60 but p = 4.5 is not an integer → not viable.
- (6, 6): 12(6)+5(6)=72+30=102 > 60 → exceeds budget.
- (−2, 6): h = −2 < 0 → not allowed.
- (2, 4): 12(2)+5(4)=24+20=44 ≤ 60 and both nonnegative integers → viable.

Answer: (2, 4).