SOLUTION: Patricia knows that at some point during the calendar year her basic monthly telephone rate increased from $17.10 to $18.40. If she paid a total of $207.80 for basic telephone serv

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Question 487755: Patricia knows that at some point during the calendar year her basic monthly telephone rate increased from $17.10 to $18.40. If she paid a total of $207.80 for basic telephone service for the calendar year, in what month did the rate increase take effect?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
her total bill was $207.80
she had x months at a rate of $17.10
she had y months at a rate of $18.40
you have 2 equations.
x + y = 12
17.10*x + 18.40*y = 207.8
you need to solve these 2 equations simultaneously to get your answer.
we'll solve this equation by elimination.
your equations are:
x + y = 12 (equation 1)
17.10x + 18.40y = 207.8 (equation 2)
multiply both sides of equation 1 by 17.10 to get:
17.10x + 17.10y = 205.2 (equation 3)
17.10x + 18.40y = 207.8 (equation 2)
subtract equation 3 from equation 2 to get:
1.3y = 2.6
divide both sides of this equation by 1.3 to get:
y = 2
since x + y = 12, this means that:
x = 10
y = 2
substitute these values for x and y in equation 2 to get:
17.10*10 + 18.40*2 = 207.8 which becomes:
171.0 + 36.8 = 207.8 which becomes:
207.8 = 207.8
this confirms the values for x and y are good.
your answer is:
she had 10 months at $17.10 and 2 months at $18.40
the rate increase took effect in November.