document.write( "Question 198209: Suppose you have a lemonade stand, and when you charge $1 per cup of lemonade you sell 50 cups. But when you raise your price to $2 you only sell 25 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote \"C\" for number of cups, and \"P\" for the price you charge. Assume the function is linear. \n" ); document.write( "

Algebra.Com's Answer #148671 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
If I plot price on the vertical axis and # of cups
\n" ); document.write( "on the horizontal axis, I have 2 points given:
\n" ); document.write( "(50,1) and (25,2)
\n" ); document.write( "The formula to use is:
\n" ); document.write( " $\"%28P+-+2%29+%2F+%28C+-+25%29+=+%281+-+2%29+%2F+%2850+-+25%29\"$
\n" ); document.write( " $\"%28P+-+2%29+%2F+%28C+-+25%29+=+-1+%2F+25\"$
\n" ); document.write( "Multiply both sides by $\"25%2A%28C+-+25%29\"$
\n" ); document.write( " $\"25%2A%28P+-+2%29+=+-1%2A%28C+-+25%29\"$
\n" ); document.write( " $\"25P+-+50+=+-C+%2B+25\"$
\n" ); document.write( " $\"25P+=+-C+%2B+75\"$
\n" ); document.write( " $\"P+=+%28-1%2F25%29%2AC+%2B+3\"$ answer
\n" ); document.write( "check:
\n" ); document.write( "does the line go through (50,1) and (25,2)?
\n" ); document.write( " $\"25P+=+-C+%2B+75\"$
\n" ); document.write( " $\"25%2A1+=+-50+%2B+75\"$
\n" ); document.write( " $\"25+=+25\"$
\n" ); document.write( "OK
\n" ); document.write( " $\"25P+=+-C+%2B+75\"$
\n" ); document.write( " $\"25%2A2+=+-25+%2B+75\"$
\n" ); document.write( " $\"50+=+50\"$
\n" ); document.write( "OK
\n" ); document.write( "Here's the plot:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-10%2C+100%2C+-1%2C+6%2C+-x%2F25+%2B+3%29\"$ \n" ); document.write( "

\n" );