document.write( "Question 1026520: Three friends each have different monthly payment plans for sending text messages.
\n" ); document.write( " Naomi pays a flat fee of $30 for an unlimited number of text messages.
\n" ); document.write( " Tina pays a base fee of $6.00 plus $0.10 per text message.
\n" ); document.write( " Chris pays a base fee plus $0.05 per text message. Last month, he paid $18.00 for 100 text
\n" ); document.write( "messages.
\n" ); document.write( "Naomi researched how much she would have to pay if she switched to Tina or Chris's plan. She
\n" ); document.write( "decided that her plan is the least expensive based on the number of text messages she uses each
\n" ); document.write( "month. What is the minimum number of text messages Naomi must use each month for her plan to be
\n" ); document.write( "the least expensive? \n" ); document.write( "

Algebra.Com's Answer #641790 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+P+\"$ = the cost of a plan
\n" ); document.write( "Let $\"+n+\"$ = the number of text messages
\n" ); document.write( "------------------------------------
\n" ); document.write( "First find Chris's base fee:
\n" ); document.write( "Let her base fee = $\"+x+\"$
\n" ); document.write( " $\"+18+=+x+%2B+.05%2A100++\"$
\n" ); document.write( " $\"+x+%2B+5+=+18+\"$
\n" ); document.write( " $\"+x+=+13+\"$
\n" ); document.write( "So, Chris's equation for her plan is:
\n" ); document.write( " $\"+P+=+13+%2B+.05n+\"$
\n" ); document.write( "Naomi's equation is:
\n" ); document.write( " $\"+P+=+30+\"$
\n" ); document.write( "Tina's equation is:
\n" ); document.write( " $\"+P+=+6+%2B+.1n+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "Find the smallest $\"+n+\"$ so that $\"+P+\"$
\n" ); document.write( "is smallest for Naomi
\n" ); document.write( "------------------
\n" ); document.write( "For what $\"+n+\"$ , does Tina pay same as Naomi?
\n" ); document.write( " $\"+6+%2B+.1n+=+30+\"$
\n" ); document.write( " $\"+.1n+=+24+\"$
\n" ); document.write( " $\"+n+=+240+\"$
\n" ); document.write( "------------------
\n" ); document.write( "For what $\"+n+\"$ , does Chris pay same as Naomi?
\n" ); document.write( " $\"+13+%2B+.05n+=+30+\"$
\n" ); document.write( " $\"+.05n+=+17+\"$
\n" ); document.write( " $\"+n+=+340++\"$
\n" ); document.write( "-------------
\n" ); document.write( "341 text messages is the least she can send and
\n" ); document.write( "be less expensive
\n" ); document.write( "---------------------
\n" ); document.write( "check:
\n" ); document.write( "Chris's equation for her plan is:
\n" ); document.write( " $\"+P+=+13+%2B+.05n+\"$
\n" ); document.write( " $\"+P+=+13+%2B+.05%2A340+\"$
\n" ); document.write( " $\"+P+=+13+%2B+17+\"$
\n" ); document.write( " $\"+P+=+30+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "Naomi:
\n" ); document.write( " $\"+P+=+30+\"$
\n" ); document.write( "--------------
\n" ); document.write( "Tina's equation is:
\n" ); document.write( " $\"+P+=+6+%2B+.1n+\"$
\n" ); document.write( " $\"+P+=+6+%2B+.1%2A340+\"$
\n" ); document.write( " $\"+P+=+6+%2B+34+\"$
\n" ); document.write( " $\"+P+=+40+\"$
\n" ); document.write( "----------------
\n" ); document.write( "If 341 texts are sent:
\n" ); document.write( "Chris:
\n" ); document.write( " $\"+P+=+30.05+\"$
\n" ); document.write( "Naomi:
\n" ); document.write( " $\"+P+=+30+\"$
\n" ); document.write( "Tina:
\n" ); document.write( " $\"+P+=+40.1+\"$
\n" ); document.write( "Naomi is less expensive \n" ); document.write( "

\n" );