Question

Sierra needs to buy batteries for her school’s emergency preparation packs. She can buy them in packs of 4 or in packs of 12, and she wants at least 100 batteries. Write a two-variable inequality to represent the situation and determine its constraints. Which of the following points represents a viable solution?(1 point)
Responses

(6,9.5)
left parenthesis 6 comma 9.5 right parenthesis

(−7,15)
left parenthesis negative 7 comma 15 right parenthesis

(2,6)
left parenthesis 2 comma 6 right parenthesis

(2,10)

Answer 1

Let x = number of 4-packs and y = number of 12-packs. The battery requirement is
4x + 12y ≥ 100,
with constraints x ≥ 0, y ≥ 0 and x, y must be whole numbers (you can't buy fractional packs). (You can also write this as x + 3y ≥ 25.)

Check the choices:
- (6, 9.5): 4(6)+12(9.5)=138 ≥100 but y is not an integer → not allowed.
- (−7, 15): x is negative → not allowed.
- (2, 6): 4(2)+12(6)=80 <100 → not enough batteries.
- (2, 10): 4(2)+12(10)=128 ≥100 and both are nonnegative integers → viable.

So (2, 10) is the valid solution.