Question

A party planner is reserving rooms for a corporate event and has at most $1,700 to spend on renting the space. The Sunrise Room costs $190 per hour and the Twilight Room costs $160 per hour.
Write 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 express the situation as an inequality, we need to account for the total cost of renting both the Sunrise Room and the Twilight Room, and ensure that this total cost does not exceed the budget of $1,700.

Given:
- The cost of the Sunrise Room is $190 per hour, which contributes \(190x\) to the total cost, where \(x\) is the number of hours the Sunrise Room is reserved.
- The cost of the Twilight Room is $160 per hour, which contributes \(160y\) to the total cost, where \(y\) is the number of hours the Twilight Room is reserved.

The inequality representing the constraint on the total cost can be written as:

\[
190x + 160y \leq 1700
\]

To express this in standard form (Ax + By ≤ C), we would leave the inequality as is since it already conforms to the standard form. Here, \(A = 190\), \(B = 160\), and \(C = 1700\).

So the final inequality in standard form is:

\[
190x + 160y \leq 1700
\]