A party planner is reserving rooms for a corporate event and has at most $1,000 to spend on renting the space. The Sunrise Room costs $130 per hour and the Twilight Room costs $260 per hour.

Question

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of hours the Sunrise Room is reserved
y = the number of hours the Twilight Room is reserved

Answer 1

To create an inequality that describes the budget constraint for reserving rooms, we need to consider the costs of renting the rooms based on the hours reserved.

Let:

• \( x \) = the number of hours the Sunrise Room is reserved
• \( y \) = the number of hours the Twilight Room is reserved

The cost of reserving the Sunrise Room for \( x \) hours is \( 130x \) (since it costs $130 per hour), and the cost of reserving the Twilight Room for \( y \) hours is \( 260y \) (since it costs $260 per hour).

The total cost for renting both rooms must be less than or equal to the budget of $1,000. Therefore, we can express this relationship as the inequality:

\[ 130x + 260y \leq 1000 \]

This inequality is already in standard form. It specifies that the total cost of renting the rooms for the specified hours should not exceed $1,000.