document.write( "Question 1010453: There is an initiation fee to join the Wellness Center, as well as monthly dues. The total cost after 7 months' membership will be $335, and after 1 1/2 year, $830. Find both the initiation fee and the monthly dues. Setup a system of equations and solve. Label your answers. Show step by step.\r
\n" ); document.write( "\n" ); document.write( "Thanks in advance! \n" ); document.write( "

Algebra.Com's Answer #625887 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
This is a straight line relation and the slope is
\n" ); document.write( "[ dues ] / [ month ]
\n" ); document.write( "Let $\"+C+\"$ = total cost including initiation plus dues
\n" ); document.write( "Let $\"+n+\"$ = number of months the dues are paid
\n" ); document.write( "-----------------------------------------
\n" ); document.write( "Plot $\"+C+\"$ on the vertical axis and
\n" ); document.write( "plot $\"+n+\"$ on the horizontal axis
\n" ); document.write( "------------------------------
\n" ); document.write( "You are given the points:
\n" ); document.write( "( 7, 335 )
\n" ); document.write( "( 18, 830 )
\n" ); document.write( "Use the general point-slope formula
\n" ); document.write( " $\"+%28+C+-+335+%29+%2F+%28+n+-+7+%29+=+%28+830+-+335+%29+%2F+%28+18+-+7+%29+\"$
\n" ); document.write( " $\"+%28+C+-+335+%29+%2F+%28+n+-+7+%29+=+495+%2F+11+\"$
\n" ); document.write( " $\"+11%2A%28+C+-+335+%29+=+495%2A%28+n+-+7+%29+\"$
\n" ); document.write( " $\"+11C+-+3685+=+495n+-+3465+\"$
\n" ); document.write( " $\"+11C+=+495n+%2B+220+\"$
\n" ); document.write( " $\"+C+=+45n+%2B+20+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "check answer:
\n" ); document.write( "( 7, 335 )
\n" ); document.write( " $\"+C+=+45n+%2B+20+\"$
\n" ); document.write( " $\"+335+=+45%2A7+%2B+20+\"$
\n" ); document.write( " $\"+335+=+315+%2B+20+\"$
\n" ); document.write( " $\"+335+=+335+\"$
\n" ); document.write( "and
\n" ); document.write( "( 18, 830 )
\n" ); document.write( " $\"+C+=+45n+%2B+20+\"$
\n" ); document.write( " $\"+830+=+45%2A18+%2B+20+\"$
\n" ); document.write( " $\"+830+=+810+%2B+20+\"$
\n" ); document.write( " $\"+830+=+830+\"$
\n" ); document.write( "OK
\n" ); document.write( "--------------------
\n" ); document.write( "The monthly dues is the slope of the line, so
\n" ); document.write( "dues = $45
\n" ); document.write( "The initiation fee is the intercept on the vertical
\n" ); document.write( "axis, found by setting $\"+n+=+0+\"$
\n" ); document.write( " $\"+C+=+45%2A0+%2B+20+\"$
\n" ); document.write( " $\"+C+=+20+\"$ , so
\n" ); document.write( "initiation = $20
\n" ); document.write( "---------------
\n" ); document.write( "Here's the plot:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-2%2C+20%2C+-100%2C+1000%2C+45x+%2B+20+%29+\"$
\n" ); document.write( "Here's a close-up of the C-intercept:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-1%2C+2%2C+-3%2C+30%2C+45x+%2B+20+%29+\"$ \n" ); document.write( "

\n" );