document.write( "Question 68852: Suppose you have a lemonade stand, and when you charge 2 dollars per cup of lemonade you sell 120 cups. But when you raise your price to 3 dollars you only sell 60 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote \"C\" for the number of cups, and \"P\" for the price you charge. Assume the function is linear. \n" ); document.write( "

Algebra.Com's Answer #49069 by josmiceli(19441) $\"\"$ $\"About$

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The key to this one is that it is linear. You can then use a
\n" ); document.write( "formula for the slope of a straight line
\n" ); document.write( "As the price goes up, you sell less cups
\n" ); document.write( "$2/cup --- 120 cups
\n" ); document.write( "$3/cup --- 60 cups
\n" ); document.write( "Let c = number of cups sold
\n" ); document.write( "Let p = price per cup
\n" ); document.write( "c will take the place of y
\n" ); document.write( "and p will take the place of x in the formula
\n" ); document.write( "

\n" ); document.write( " $\"%28c+-+120%29+%2F+%28p+-+2%29+=+%2860+-+120%29+%2F+%283+-+2%29\"$
\n" ); document.write( " $\"%28c+-+120%29+%2F+%28p+-+2%29+=+%28-60%29+%2F+1\"$
\n" ); document.write( " $\"c+-+120+=+-60p+%2B+120\"$
\n" ); document.write( " $\"c+=+%28-60%29p+%2B+240\"$ answer
\n" ); document.write( "check it
\n" ); document.write( "p = 3
\n" ); document.write( " $\"c+=+%28-60%29%2A3+%2B+240\"$
\n" ); document.write( " $\"c+=+60\"$
\n" ); document.write( "OK
\n" ); document.write( "p = 2
\n" ); document.write( " $\"c+=+%28-60%29%2A2+%2B+240\"$
\n" ); document.write( " $\"c+=+120\"$
\n" ); document.write( "Note that if you sell for $4/cup, you won't sell any cups \n" ); document.write( "

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