SOLUTION: subscription rate for basic cable increased from $18.50 TO $19.50 AT SOME POINT DURING THE YEAR. Paid a total 0f $230.10 for the year. determine the month of the increase.

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Question 1100508: subscription rate for basic cable increased from $18.50 TO $19.50 AT SOME POINT DURING THE YEAR. Paid a total 0f $230.10 for the year. determine the month of the increase.
Answer by Theo(13342) About Me  (Show Source):
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let x = the number of months at 18.5
let y = the number of months at 19.5

18.5 * x + 19.5 * y = 230.1

x + y = 12

solve for x to get x = 12 - y

18.5 * (12 - y) + 19.5 * y = 230.1

simplify to get 222 - 18.5y + 19.5y = 230.1

combine line terms and subtract 222 from both sides of the equation to get:

y = 8.1

since x + y = 12, then x = 3.9

18.5 * 3.9 + 19.5 * 8.1 = 230.1

at the end of 3, you enter the fourth month.
at the end of 4, you enter the fifth month.

the increase was towards the end of the fourth month.