Question

Mary is buying snacks at the grocery store. Cookies cost $0.75 each and bags of chips cost $1.25 each. She plans to spend no more than $10 but wants to buy at least 12 snacks. She uses the variables x=total cookies bought and y=total bags chips bought. Would you categorize the point
(
11.5
,
1
)
as a viable solution, a nonviable solution, or not a solution to the system of linear inequalities that would represent this situation? Explain.(1 point)
Responses

The point
(
11.5
,
1
)
is nonviable because you can only buy whole- number amounts of bags of chips.
The point left parenthesis 11.5 comma 1 right parenthesis is nonviable because you can only buy whole- number amounts of bags of chips.

The point
(
11.5
,
1
)
is nonviable because you can only buy whole-number amounts of cookies.
The point left parenthesis 11.5 comma 1 right parenthesis is nonviable because you can only buy whole-number amounts of cookies.

The point
(
11.5
,
1
)
is not a solution to this problem because it lies outside of the overlapping shaded region of the graph.
The point left parenthesis 11.5 comma 1 right parenthesis is not a solution to this problem because it lies outside of the overlapping shaded region of the graph.

The point
(
11.5
,
1
)
is a viable solution because it lies within the overlapping shaded region of the graph.

Answer 1

The point \( (11.5, 1) \) is nonviable because you can only buy whole-number amounts of cookies and bags of chips.

In the context of this problem, since \( x \) (cookies) and \( y \) (bags of chips) must be non-negative integers, having a non-integer value for \( x \) (11.5) makes this point invalid for this scenario. Therefore, the correct explanation is:

The point \( (11.5, 1) \) is nonviable because you can only buy whole-number amounts of cookies.