SOLUTION: A local arcade offers 2 packages. You can either pay $30 a month for unlimited games or pay a monthy fee of $10.50 plus $0.75 per game. Write an equation that shows the number of

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A local arcade offers 2 packages. You can either pay $30 a month for unlimited games or pay a monthy fee of $10.50 plus $0.75 per game. Write an equation that shows the number of      Log On


   



Question 1082156: A local arcade offers 2 packages. You can either pay $30 a month for unlimited games or pay a monthy fee of $10.50 plus $0.75 per game.
Write an equation that shows the number of games played and the cost of each membership if you pay $30 a month for unlimited games or $10.50 a month plus $0.75 per game.
What is the slope of each equation?
What information does the slope of each line represent in this context?
What is the Y-intercept in each equation?
What information does the Y-intercept of each line represent in this context?
When will the cost be the same?
Explain how to find from a table, a graph, and an equation.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +y+ = monthly cost
Let +x+ = number of games played
1st package:
+y+=+30+
2nd package:
+y+=+.75x+%2B+10.5+
---------------------
(1)
The slope for 1st package is zero
The slope for 2nd package is +.75+
-----------------------------------
(2)
The slope shows how fast the cost is
change from month to month
-----------------------------------
(3)
1st package:
y-intercept = 30
2nd package:
y-intercept = .75
---------------------
The y-intercept is the fixed cost before any
games are played
----------------------
When will the cost be the same?
[ 1st package ] = [ 2nd package ]
+30+=+.75x+%2B+10.5+
+.75x+=+19.5+
+x+=+26+
The cost is the same when 26 games are played
After that the 2nd package will cost more than
the 1st
---------------------
Here's the plot:
+graph%28+400%2C+400%2C+-3%2C+40%2C+-4%2C+40%2C+30%2C+.75x+%2B+10.5+%29+