The 2017 Wyoming state senate had 30 elected members consisting of Democrats and Republicans. Let d represent the number of Democrats who vote yes for a bill, and let r represent the number of Republicans who vote yes for a bill. For a bill to pass, more than half of the 30 senators must vote yes. Which of the following inequalities represents all possible values of d and r for a bill to pass?

The correct answer is:

Different types of inequalities:
x is more than , i.e., ; x is less than , i.e., x < y.
x is more than or equal to y, i.e., ; x is less than or equal to y, i.e., .
Explanations:
Step 1 of 2:
Let d represents the number of Democrats who vote yes for a bill.
Let r denotes the number of Republicans who vote yes for a bill.
For a bill to pass, more than half of the 30 senators must vote yes. So, half of 30 senators is 15.
Step 2 of 2:
The 2017 Wyoming state senate had 30 elected members consisting of Democrats and Republicans.
So, to pass a bill, 16 to 30 members must vote yes.
The total number of members, consisting of Democrats and Republicans, voted yes, is .
Hence, the inequality should be .
According to the given inequalities, the option satisfies the conditions.
Final Answer:
The inequality represents all possible values of and for a bill to pass — .