Alejandro is saving all the money he earned from working on chores this year. He has a combination of $1 bills and $5 bills in his safe. Alejandro knows that he has earned at least $100, and he has less than a total of 60 bills in his safe. If x represents the total amount of $1 bills and y represents the total amount of $5 bills, is the point (30,22.5)

Question

(
30
,
22.5
)
a viable solution? Explain.(1 point)
Responses

No, because y represents the total number of $5 bills. You cannot have a half bill.
No, because y represents the total number of $5 bills. You cannot have a half bill.

Yes, because the point (30,22.5)
(
30
,
22.5
)
lies within the overlapping shaded region of the graph.
Yes, because the point left parenthesis 30 comma 22.5 right parenthesis lies within the overlapping shaded region of the graph.

Yes, because the point (30,22.5)
(
30
,
22.5
)
satisfies both inequalities.
Yes, because the point left parenthesis 30 comma 22.5 right parenthesis

Answer 1

The correct response is:

No, because y represents the total number of $5 bills. You cannot have a half bill.

The values of x (the number of $1 bills) and y (the number of $5 bills) must be non-negative integers. Since y is given as 22.5 in the point (30, 22.5), this indicates that Alejandro would have a fractional number of $5 bills, which is not possible. Therefore, the point (30, 22.5) is not a viable solution.