document.write( "Question 1170779: Some students at L.C.V.I. held a bake sale
\n" ); document.write( "recently to raise money for a field trip.
\n" ); document.write( "They charged $7 for fruit pies and $10 for
\n" ); document.write( "meat pies. They sold a total of 52 pies and
\n" ); document.write( "earned $424. How many of each type of
\n" ); document.write( "pie did they sell? \n" ); document.write( "
Algebra.Com's Answer #795672 by greenestamps(13200)\"\" \"About 
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\n" ); document.write( "A setup using formal algebra....

\n" ); document.write( "f = # of fruit pies
\n" ); document.write( "m = # of meat pies

\n" ); document.write( "The total sales, at $7 for each fruit pie and $10 for each meat pie, was $424:

\n" ); document.write( "(1) \"7f%2B10m+=+424\"

\n" ); document.write( "The total number of pies was 52:

\n" ); document.write( "(2) \"f%2Bm=52\"

\n" ); document.write( "One possible way to solve this pair of equation is to multiply the second equation by 10 and compare the resulting equation to (1):

\n" ); document.write( "\"10f%2B10m+=+520\"
\n" ); document.write( "\"7f%2B10m+=+424\"
\n" ); document.write( "\"3f+=+96\" (the difference between those two equations)
\n" ); document.write( "\"f+=+32\"

\n" ); document.write( "ANSWER: the number of fruit pies sold was 32; the number of meat pies was 52-32=20.

\n" ); document.write( "You can solve the problem informally, using EXACTLY the same calculations, like this:

\n" ); document.write( "(1) If all 52 pies were meat pies, the total sales would be $520.
\n" ); document.write( "(2) The actual total sales was $424, which is $96 less than $520.
\n" ); document.write( "(3) Each fruit pie costs $3 less than each meat pie.
\n" ); document.write( "(4) The number of fruit pies sold, to bring the sales total down $96, from $520 to $424, is $96/$3 = 32.

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