Ms. Hurst is planning a dance recital for her students. The maximum duration for the recital is 87 minutes. Group dance numbers last 4 minutes and a solo performance lasts 3 minutes. Which inequality (in standard form) describes this situation. Use the given numbers and the following variables.
x = the number of group dances on the program
y = the number of solo numbers on the program
4x+3y<87 3x+4y≤87 3x+4y<87 4x+3y≤87
Convert each inequality into Slope-Intercept Form.
Determine which one matches the situation.
Graph the inequality.
Choose 2 solutions for the inequality, written in context.
Explain, in detail and using academic language, how you found your solution.

Inequality is

Slope intercept form is

Solutions are

Graph: attached to the question

Step-by-step explanation:

Given: Group dance numbers last 4 minutes and a solo performance lasts 3 minutes. The maximum duration for the recital is 87 minutes.

To find: inequality (in standard form) that describes the given situation, inequality in slope-intercept form, solutions for the inequality

To graph: the inequality

Solution:

x denotes the number of group dances on the program

y denotes the number of solo numbers on the program

Total duration of group dance numbers = minutes

Total duration of solo performance = minutes

According to question,

Slope intercept form of equation is where m denotes slope of line and c denotes y-intercept of the line.

Slope intercept form of :

For ,

So, is a solution of the inequality.

For ,

So, is a solution of the inequality.

Graph: attached as image

x=6 and x=3

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