Question

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.

Answer 1

Answer:

Inequality is $4x+3y\leq 87$

Slope intercept form is $y\leq 29-\frac{4}{3}x$

Solutions are $(2,3)\,,\,(3,4)$

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 = $4x$ minutes

Total duration of solo performance = $3y$ minutes

According to question,

$4x+3y\leq 87$

Slope intercept form of equation is $y\leq mx+c$ where m denotes slope of line and c denotes y-intercept of the line.

Slope intercept form of $4x+3y\leq 87$ :

$4x+3y\leq 87\\3y\leq 87-4x\\y\leq 29-\frac{4}{3}x$

For $(x,y)=(2,3)$,

$4(2)+3(3)\leq 87\\8+9\leq 87\\17\leq 87\,\,which\,\,is\,\,true$

So, $(2,3)$ is a solution of the inequality.

For $(x,y)=(3,4)$,

$4(3)+3(4)\leq 87\\12+12\leq 87\\24\leq 87\,\,which\,\,is\,\,true$

So, $(3,4)$ is a solution of the inequality.

Graph: attached as image

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