Saturday, January 27, 2007

L's Problem of the Week: The Phone Dilemma

You have a vacation home in Vermont (I keep picturing Killington because I had to go to this conference there in November). You have a choice of two phone providers: VTT and VP.

VP rates: $30 installation and 12¢a minute.
VTT: $50 installation and 9¢a minute.

What is the best buy? (Installation charges are one time fee. But can we assume that summer people just have the one installation? Or do the phone companies charge the fee every year?)

We need at least 3 methods to solve the problem: graphing, a table, and simultaneous equations.

The graph is above BUT I can't figure out in this new version
of Excel that I have how to adjust the scale. As soon as I get my hands on the older version on Monday, I'll fix it up in a jiffy.


The equations:
VP: y = 30 + 0.12x
VTT: y = 50 + 0.09x

3(y = 30 + 0.12x)
-4(y = 50 + 0.09x)

3y = 90 + 0.36x
-4y = -200 - 0.36x

-y = -110
y = 110

if y = 110, then:
110 = 30 + 0.12x
80 = 0.12x
666.67 = x

The graphs will intersect at (666.67 minutes, $110)

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