Question

An event planner is reserving rooms for a company-wide event. Each ballroom can hold 84 people and each conference room can hold 19 people, and together they must hold at least the 958 people participating.
Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of ballrooms
y = the number of conference rooms

Answer 1

To represent the situation with an inequality in standard form, we need to express the total capacity of the ballrooms and conference rooms in relation to the number of participants.

Let:
- \( x \) = the number of ballrooms
- \( y \) = the number of conference rooms

Each ballroom can hold 84 people, so the total capacity from the ballrooms can be represented as \( 84x \).

Each conference room can hold 19 people, so the total capacity from the conference rooms can be represented as \( 19y \).

The total capacity must be at least 958 people, which gives us the inequality:
\[
84x + 19y \geq 958
\]

To express this in standard form (generally, Ax + By ≥ C), we can write it as:
\[
84x + 19y - 958 \geq 0
\]

So, the inequality in standard form is:
\[
84x + 19y \geq 958
\]