An event planner is reserving rooms for a company-wide event. Each ballroom can hold 93 people and each conference room can hold 23 people, and together they must hold at least the 841 people participating. Select 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 Choices: (A)23x - 93y ≥ 841 (B)93x + 23y ≥ 841 (C)93x * 23y ≥ 841 (D)23x + 93y ≥ 841

Determine Capacity: Determine the capacity of each type of room. We are given that each ballroom can hold 93 people and each conference room can hold 23 people. The variables x and y represent the number of ballrooms and conference rooms, respectively. Therefore, the total capacity of ballrooms is 93x and the total capacity of conference rooms is 23y.Combine Capacities: Combine the capacities to represent the total capacity. Since we want to find the total number of people that can be accommodated by x ballrooms and y conference rooms, we add the capacities together to get the total capacity, which is 93x + 23y.Set Up Inequality: Set up the inequality based on the requirement. We know that the total number of people attending is at least 841, which means the combined capacity of ballrooms and conference rooms must be greater than or equal to 841. This gives us the inequality 93x + 23y ≥ 841.Match to Choices: Match the inequality to the given choices. The inequality we have found, 93x + 23y ≥ 841, corresponds to choice (B) from the given options.

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An event planner is reserving rooms for a company-wide event. Each ballroom can hold $93$ people and each conference room can hold $23$ people, and together they must hold at least the $841$ people participating. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of ballrooms $\newline$ $y =$ the number of conference rooms $\newline$ Choices: $\newline$ (A) $23x - 93y \geq 841$ $\newline$ (B) $93x + 23y \geq 841$ $\newline$ (C) $93x \times 23y \geq 841$ $\newline$ (D) $23x + 93y \geq 841$

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Algebra 1

Write two-variable inequalities: word problems

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Q. An event planner is reserving rooms for a company-wide event. Each ballroom can hold

93

people and each conference room can hold

23

people, and together they must hold at least the

841

people participating.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of ballrooms

\newline

y =

the number of conference rooms

\newline

Choices:

\newline

(A)

23x - 93y \geq 841

\newline

(B)

93x + 23y \geq 841

\newline

(C)

93x \times 23y \geq 841

\newline

(D)

23x + 93y \geq 841

Determine Capacity: Determine the capacity of each type of room. We are given that each ballroom can hold $93$ people and each conference room can hold $23$ people. The variables $x$ and $y$ represent the number of ballrooms and conference rooms, respectively. Therefore, the total capacity of ballrooms is $93x$ and the total capacity of conference rooms is $23y$ .
Combine Capacities: Combine the capacities to represent the total capacity. Since we want to find the total number of people that can be accommodated by $x$ ballrooms and $y$ conference rooms, we add the capacities together to get the total capacity, which is $93x + 23y$ .
Set Up Inequality: Set up the inequality based on the requirement. We know that the total number of people attending is at least $841$ , which means the combined capacity of ballrooms and conference rooms must be greater than or equal to $841$ . This gives us the inequality $93x + 23y \geq 841$ .
Match to Choices: Match the inequality to the given choices. The inequality we have found, $93x + 23y \geq 841$ , corresponds to choice $(B)$ from the given options.