document.write( "Question 1209265: In one month a store sold pads of paper, some for $14, some for $5 and some for 50¢. A total of 54 pads were sold for a total of $54. Evaluate the total number of the 50¢ pads sold minus the number of $5 pads sold.
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Algebra.Com's Answer #847939 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "x = # of $14 pads
\n" ); document.write( "y = # of $5 pads
\n" ); document.write( "z = # of 50-cent pads

\n" ); document.write( "The total number of pads was 54:
\n" ); document.write( " $\"x%2By%2Bz=54\"$

\n" ); document.write( "The total cost was $54:
\n" ); document.write( " $\"14x%2B5y%2B.5z=54\"$

\n" ); document.write( "With the equations in this form, I find it easiest to solve using elimination.

\n" ); document.write( "Multiply the second equation by 2 and compare to the first using subtraction:

\n" ); document.write( " $\"28x%2B10y%2Bz=108\"$
\n" ); document.write( " $\"x%2By%2Bz=54\"$
\n" ); document.write( " $\"27x%2B9y=54\"$
\n" ); document.write( " $\"3x%2By=6\"$

\n" ); document.write( "There are formal methods for finding the complete set of solutions to this equation. However, since the numbers are small and all unknowns have positive integer values, the solution is simple -- the only solution in positive integers is x=1 and y=3, which leads to z=50.

\n" ); document.write( "# of $14 pads: 1
\n" ); document.write( "# of $5 pads: 3
\n" ); document.write( "# of 50-cent pads: 50

\n" ); document.write( "ANSWER: 50-3 = 47

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