document.write( "Question 1096313: Polar Treats sells one-dip ice cream cones for $2.25, two-dip cones for $3.15, and three dip-cones for $3.85. On Saturday, they sold 200 cones for a total of $599.20. Altogether, Polar Treats used 380 dips of ice cream. How many of each size cone were sold? \n" ); document.write( "

Algebra.Com's Answer #710749 by josmiceli(19441) $\"\"$ $\"About$

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I get it that each cone can have either 1, 2, or 3 dips
\n" ); document.write( "Let $\"+a+\"$ = number of 1-dip cones sold on Sat.
\n" ); document.write( "Let $\"+b+\"$ = number of 2-dip cones sold on Sat.
\n" ); document.write( "Let $\"+c+\"$ = number of 3-dip cones sold on Sat.
\n" ); document.write( "-----------------------------------------------
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+200+\"$
\n" ); document.write( "(2) $\"+1%2Aa+%2B+2%2Ab+%2B+3%2Ac+=+380+\"$
\n" ); document.write( "(3) $\"+2.25a+%2B+3.15b+%2B+3.85c+=+599.2+\"$
\n" ); document.write( "----------------------------------------
\n" ); document.write( "(3) $\"+225a+%2B+315b+%2B+385c+=+59920+\"$
\n" ); document.write( "(3) $\"+45a+%2B+63b+%2B+77c+=+11984+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+45+\"$ and subtract
\n" ); document.write( "(1) from (3)
\n" ); document.write( "(3) $\"+45a+%2B+63b+%2B+77c+=+11984+\"$
\n" ); document.write( "(1) $\"+-45a+-+45b+-+45c+=+-9000+\"$
\n" ); document.write( "------------------------------------
\n" ); document.write( " $\"+18b+%2B+32c+=+2984+\"$
\n" ); document.write( "(4) $\"+9b+%2B+16c+=+1492+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "(2) $\"+a+%2B+2b+%2B+3c+=+380+\"$
\n" ); document.write( "(1) $\"+-a+-+b+-+c+=+-200+\"$
\n" ); document.write( "---------------------------
\n" ); document.write( "(5) $\"+b+%2B+2c+=+180+\"$
\n" ); document.write( "Multiply both sides of (5) by $\"+8+\"$
\n" ); document.write( "and subtract (5) from (4)
\n" ); document.write( "(4) $\"+9b+%2B+16c+=+1492+\"$
\n" ); document.write( "(5) $\"+-8b+-+16c+=+-1440+\"$
\n" ); document.write( "---------------------------
\n" ); document.write( " $\"+b+=+52+\"$
\n" ); document.write( "and
\n" ); document.write( "(4) $\"+9%2A52+%2B+16c+=+1492+\"$
\n" ); document.write( "(4) $\"+468+%2B+16c+=+1492+\"$
\n" ); document.write( "(4) $\"+16c+=+1024+\"$
\n" ); document.write( "(4) $\"+c+=+64+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+%2B+52+%2B+64+=+200+\"$
\n" ); document.write( "(1) $\"+a+=+200+-+116+\"$
\n" ); document.write( "(1) $\"+a+=+84+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "They sold:
\n" ); document.write( "84 1-dip cones
\n" ); document.write( "52 2-dip cones
\n" ); document.write( "64 3-dip cones
\n" ); document.write( "----------------------
\n" ); document.write( "check:
\n" ); document.write( "(3) $\"+2.25a+%2B+3.15b+%2B+3.85c+=+599.2+\"$
\n" ); document.write( "(3) $\"+2.25%2A84+%2B+3.15%2A52+%2B+3.85%2A64+=+599.2+\"$
\n" ); document.write( "(3) $\"+189+%2B+163.8+%2B+246.4+=+599.2+\"$
\n" ); document.write( "(2) $\"+599.2+=+599.2+\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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