Question 1166854: A cellular phone company charges $63.95 per month for a service plan that includes 6 GB of data. In addition to the basic monthly rate, the company charges $7.95 for each additional GB of data over 6 GB. A customer on this plan receives a bill for $119.60. How much data did this customer send and receive during the month?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the basic charge is 63.95 per month.
this includes 6 GB of data.
the company also charges $7.95 for each GB of data over 6 GB.
the customer receives a bill foro $119.60.
subtract 63.95 from this to get 55.65 in charges for data use over 6 GB.
divide 55.65 by 7.95 to get 7 GB of data over the free allowance of 6 GB.
this means the customer used a total of 6 + 7 = 13 GB of data during the month.
if you made a piecewise function to model this, that function would look like this.
y = 63.95 for x <= 6
y = 63.95 + 7.95 * (x - 6) for x > 6
in this piecewise function, the value of x is the total GB of data used.
when x = 13, the second piecewise function would be used.
you would then get y = 63.95 + 7.95 * (13 - 6) = 119.6
since you know y, but don't know x, you would assume the second function because y > 63.95 indicates additional usage of data over the minimum.
the second function becomes.
119.6 = 63.95 + 7.95 * (x - 6)
simplify this to get:
119.6 = 63.95 + 7.95 * x - 47.7
combine like terms to get:
119.6 = 7.95 * x + 16.25
subtract 16.25 from both sides of the equation to get:
103.35 = 7.95 * x
solve for x to get:
x = 103.35 / 7.95 = 13.
that means that the total number of GB used during the month is 13.
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