Final answer:
The inequality representing all possible combinations of upper deck (U) and lower deck (I) tickets with a $650 budget is 150I + 0.7U ≤ 650, which corresponds to option A.
Step-by-step explanation:
The student is looking to find which inequality represents all the possible combinations of upper deck tickets, denoted as U, and lower deck tickets, denoted as I, that could be purchased with a budget of $650. Given that lower deck seats cost $150 each, and upper deck seats cost 70% of the lower deck seats, the cost for an upper deck seat would be $150 × 70% = $105. So, we calculate the cost using these values to get the inequality.
We can set up the inequality by multiplying the number of lower deck tickets (I) by their price ($150) and adding this to the number of upper deck tickets (U) multiplied by their price ($105). The sum should be less than or equal to the total budget of $650. This is represented by the inequality 150I + 105U ≤ 650. However, since the options do not include these exact numbers and instead use a decimal for the upper deck cost, we convert $105 to 70% of $150, which is 0.7 times $150. Therefore, the correct inequality from the given options is 150I + 0.7U ≤ 650, matching option A.