Question

Tara teaches ballet in groups of two students. She rents a room for the ballet classes at $350 per month. She charges $50 per hour per student. Tara teaches five groups of students, and her net earnings per month are $3,150.

If each student learns ballet for the same number of hours, write an equation that can be used to calculate the number of hours each student learns ballet in a month.

How many hours did each student learn ballet each month? Show your work and justify each step of your work.

Answer 1

@ranga

Answer 2

@douglaswinslowcooper can you help me PLEASE??

Answer 3

brb answering another question. The notifications is very slow. just informed me of your tagging. brb.

Answer 4

ok

Answer 5

Let x be the number of hours each student learns each month.
Then each student pays $50 per hour * x hours per month.
Each student pays 50x dollars per month.

2 students per group and 5 groups. That is a total of 2 * 5 = 10 students.
10 students will pay 10 * 50x = 500x dollars per month.

Rent per month is $350

Net earnings = 500x - 350
500x - 350 = 3,150
is the equation.

Solve for x.

Answer 6

x = 7

Answer 7

So my answer is 500x - 350 = 3,150 for the equation and each student did ballet for seven hours?

Answer 8

yes.

Answer 9

Thanks can you help me with a few more please?

Answer 10

Let us try one more. I am answering another question. After I finish that I will come back here and finish this after which I have to attend to my work.

Answer 11

Ok thanks!

Answer 12

Sam is observing the velocity of a car at different times. After three hours, the velocity of the car is 53 km/h. After six hours, the velocity of the car is 62 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used.

Part B: How can you graph the equation obtained in Part A for the first seven hours?

Answer 13

Let t represent time in hours and v represent velocity in km/h.
We have to assume the velocity increases linearly with time t. In other words, graph of velocity versus time will be s straight line.

We are given two points on the line:
when t = 3, v = 53. Therefore, (3, 53) is a point on the line
when t = 6, v = 62. Therefore, (6, 62) is another point on the line

The slope of the line = rise / run = (62 - 53) / (6 - 3) = 9 / 3 = 3
The equation of the line is v = 3t + b.
To find b, put the first point (3, 53) into the equation:
53 = 3(3) + b
53 = 9 + b
b = 53 - 9 = 44

v = 3t + 44 is the equation.

Answer 14

Got query about ballet class awhile ago x=7hr is right.

Answer 15

Yeah thanks sorry I shouldn't have tagged you I just needed some help. :) And thanks @ranga.

Answer 16

You are welcome.

To graph the equation of the straight line you really don't need the equation because we know two points on the line. Locate the two points on the graph and connect them with a straight line. The line need not extend past t = 7 hours because they want the graph for the first seven hours. But extend the line in the downward direction until it touches the x-axis. Not past the x axis because that will be negative time and we don't want that. So line should go from t = 0 to t = 7 (t will be along x-axis and v will be along y-axis).

Answer 17

Ok thanks do you have time for one more short one?

Answer 18

@douglaswinslowcooper can you help me with a question?

Answer 19

Please (showing you my big brown puppy dog eyes, lol)

Answer 20

Well you are not answering me so I am just going to ask it anyways.


The table below shows the outputs y for different inputs x:

Input
(x) 1 1 3 3
Output
(y) 4 2 12 6

Does the table represent y as a function of x? Justify your answer.

The only reason I don't know this is because the input is not a function.

Answer 21

@amigatour can you help me?

Answer 22

@douglaswinslowcooper PLEASE help me!!!!!!!!!

Answer 23

Nevermind.

Answer 24

Sorry, I was also working on my homework. I apologize for the inconvenience.

Answer 25

It is ok I got it right :)