document.write( "Question 1150683: Jimmy has $200 to buy dessert. Pies cost $10 each, cakes $20. 1 pie feeds 12 people, 1 cake feeds 24. There are 210 people coming. Right 4 inequalities/equations.\r
\n" ); document.write( "\n" ); document.write( "- This isn't the exact problem, but all of the values and variables are correct, but I am pretty sure it is 4 equations/inequalities, and it needs to be solved. \n" ); document.write( "
Algebra.Com's Answer #772093 by greenestamps(13200)\"\" \"About 
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\n" ); document.write( "There are only two unknowns -- the number of pies and the number of cakes. With two unknowns you only need two equations or inequalities.

\n" ); document.write( "The statement of the problem doesn't make it clear whether we are to use equations or inequalities; so let's try equations first.

\n" ); document.write( "Let p = number of pies
\n" ); document.write( "Let c = number of cakes

\n" ); document.write( "The total cost of the desserts, at $10 per pie and $20 per cake, must be $200:

\n" ); document.write( "\"10p%2B20c+=+200\"

\n" ); document.write( "The number of people to be served, at 12 per pie and 24 per cake, is 210:

\n" ); document.write( "\"12p%2B24c+=+210\"

\n" ); document.write( "The first equation is equivalent to \"c%2B2p+=+20\"; the second equation is equivalent to \"c%2B2p+=+17.5\"

\n" ); document.write( "Obviously there is no common solution to those two equations.

\n" ); document.write( "So apparently we are to use inequalities -- the total cost must be AT MOST $200; and the number of people to be fed must be AT LEAST 210.

\n" ); document.write( "Then the inequalities are equivalent to \"c%2B2p+%3C=+20\" and \"c%2B2p+%3E=+17.5\".

\n" ); document.write( "And that pair of inequalities is equivalent to the compound inequality

\n" ); document.write( "\"17.5+%3C=+c%2B2p+%3C=+20\"

\n" ); document.write( "We can assume that the numbers of pies and cakes must be whole numbers. So any pair of whole numbers c and p that satisfy that inequality are the possible numbers of pies and cakes.

\n" ); document.write( "There are numerous such pairs; here are a few of them....
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document.write( "   pies  cakes        cost          people served\r\n" );
document.write( "  ----------------------------------------------------\r\n" );
document.write( "     0     9     0(10)+ 9(20) = 180   0(12)+ 9(24) = 216\r\n" );
document.write( "     0    10     0(10)+10(20) = 200   0(12)+10(24) = 240\r\n" );
document.write( "     1     9     1(10)+ 9(20) = 190   1(12)+ 9(24) = 228\r\n" );
document.write( "     2     8     2(10)+ 8(20) = 180   2(12)+ 8(24) = 216\r\n" );
document.write( "     2     9     2(10)+ 9(20) = 200   2(12)+10(24) = 264\r\n" );
document.write( "     ...\r\n" );
document.write( "    18     0    18(10)+ 0(20) = 180  18(12)+ 0(24) = 216\r\n" );
document.write( "    18     1    18(10)+ 1(20) = 200  18(12)+ 1(24) = 240\r\n" );
document.write( "     ...
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