document.write( "Question 34579: This exercise is solving applied problems: three equations.
\n" ); document.write( " Sally works at Starbucks a 10-oz cup of coffee costs $1.09, a 14-oz cup costs $1.29 and a 20-oz cup costs $1.49. During a busy period, Sally served 34 cups of coffee, emptying five 96-oz pots while collecting $43.46. How many cups of each size did Sally fill?
\n" ); document.write( " I know the answer is 8 10-oz, 20 14-oz, and 6 20-oz but how do you get those answers? \n" ); document.write( "
Algebra.Com's Answer #20892 by Paul(988)\"\" \"About 
You can put this solution on YOUR website!
Let the 10-oz cup be x
\n" ); document.write( "Let the 14-oz cup be y
\n" ); document.write( "Let the 20-oz cup be z
\n" ); document.write( "Now we know that:
\n" ); document.write( "x+y+z=34 (equation 1)
\n" ); document.write( "\"emptying five 96-oz pots...\" translate that into 5 of 96-oz pots
\n" ); document.write( "so
\n" ); document.write( "10x+14y+20z=5(96) (equation 2)
\n" ); document.write( "109x+129y+149z=4346 (equation 3)
\n" ); document.write( "Mutliply equation 1 by 14:
\n" ); document.write( "and subbtract 2 by 1:
\n" ); document.write( "10x+14y+20z=480
\n" ); document.write( "14x+14y+14z=476
\n" ); document.write( "-4x+6z=4 (equation 4)
\n" ); document.write( "Subbtract equation 2 by equation 3
\n" ); document.write( "And mutliply equation 2 by 129 and equation 3 by 14
\n" ); document.write( "1290x+1806y+2580z=61920
\n" ); document.write( "1526x+1806y+2086z=60844\r
\n" ); document.write( "\n" ); document.write( "-236x+494z=1076 (equation 5)
\n" ); document.write( "Multiply equation 4 by 236 and subbstract E5 by E4
\n" ); document.write( "-236x+494z=1076
\n" ); document.write( "-236x+354z=236
\n" ); document.write( "140z=840
\n" ); document.write( "z=6
\n" ); document.write( "
-4x+6(6)=4
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document.write( "-4x=-32
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document.write( "x=8
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document.write( "In x+y+z=34
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document.write( "8+y+6=34
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document.write( "y=20
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document.write( "Hence, their are 8 10-oz cups, 20 14-oz cups and 6 20-oz cups.
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document.write( "Paul. \r
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