Question 1026520
Let {{{ P }}} = the cost of a plan
Let {{{ n }}} = the number of text messages
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First find Chris's base fee:
Let her base fee = {{{ x }}}
{{{ 18 = x + .05*100  }}}
{{{ x + 5 = 18 }}}
{{{ x = 13 }}}
So, Chris's equation for her plan is:
{{{ P = 13 + .05n }}}
Naomi's equation is:
{{{ P = 30 }}}
Tina's equation is:
{{{ P = 6 + .1n }}}
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Find the smallest {{{ n }}} so that {{{ P }}}
is smallest for Naomi
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For what {{{ n }}}, does Tina pay same as Naomi?
{{{ 6 + .1n = 30 }}}
{{{ .1n = 24 }}}
{{{ n = 240 }}}
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For what {{{ n }}}, does Chris pay same as Naomi?
{{{ 13 + .05n = 30 }}}
{{{ .05n = 17 }}}
{{{ n = 340  }}}
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341 text messages is the least she can send and
be less expensive
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check:
Chris's equation for her plan is:
{{{ P = 13 + .05n }}}
{{{ P = 13 + .05*340 }}}
{{{ P = 13 + 17 }}}
{{{ P = 30 }}}
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Naomi:
{{{ P = 30 }}}
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Tina's equation is:
{{{ P = 6 + .1n }}}
{{{ P = 6 + .1*340 }}}
{{{ P = 6 + 34 }}}
{{{ P = 40 }}}
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If 341 texts are sent:
Chris:
{{{ P = 30.05 }}}
Naomi:
{{{ P = 30 }}}
Tina:
{{{ P = 40.1 }}}
Naomi is less expensive