i need major help with this

Question

helga is interested in adding an additional after school activity to her weekly routine.  She is interested in adding either flag football or dance. The after school flag football team costs $30 per month to participate in plus an additional $2.50 for each game played. The dance studio charges a monthly fee of $42 plus an additional  $1 for each dance class taken.  

1. write an equation that represents the monthly cost for eaxh activity. 
2. what is the total monthly cost for Helga if she takes 5 dance classes or plays 5 football games (solve both) 
3. Find how many classes or games Helga would need to take for the total monthly cost of the activities to cost the same. 
4. If you were to graph the two equations in number 1 at what coordinate would the lines intersect? what is the meaning of this intersection point in the context of this problem? 

Answer 1

1. Let x = number of football games or dances

 

    If C₁ = cost of x games in a month, then

 

          C₁ = 30 + 2.5x

 

    If C₂ = cost of x classes in a month, then

 

          C₂ = 42 + x

 

2.  Cost of 5 games = 30 + 2.5(5) =$42.50

     Cost of 5 classes = 42 + 5 = $47

 

3. The costs are the same if 30 + 2.5x = 42 + x

                                                      1.5x = 12

                                                           x = 8

 

4. When x = 8, C₁ = 30 + 2.5(8) = $50

                        C₂ = 42 + 8 = $50

 

    The graphs intersect at the point (8, 50).  This is     the point at which the monthly costs are the             same.   

Answer 2

Susana, let's take this little by little. Don't let the words get in the way!

 

Let's define our variables.  Let's let x = the number of games played monthly or the number of dance classes taken monthly and y = the total monthly charge either way.

 

If Helga plays 2 games in a month, then she pays $30 + $2.50(2), for a total of $35, right? In other words, g = 2 and m = $35.

 

1. The equation for flag football is y = $2.50x + $30, as we write the term with the variable first, backwards from what you may think.  I bet you can figure out the dance equation.

 

2. I think you can plug in the numbers like I did for 2 games and figure out both!

 

3. Remember that if two different things equal m, then they equal each other!  Once you set up your two equations, put the two things that y equals equal to each other instead and solve for x.  In other words, if a = b and a = c, then b = c, right?

 

4. Once you solve for that x in #3, plug it into either equation to get your y. Put your answer in the form of (x,y), the point where the number of activities and the monthly charge are the same.

 

To give you something to work toward, your answer to #4 is (8,50).

 

Hope this helps! I know you can do it!