document.write( "Question 1178433: A phone bill of $32.50 was paid in fifty cent pieces and quarters. the number of fifty cent pieces exceeded the number of quarter by five. how many of each were there \n" ); document.write( "

Algebra.Com's Answer #807663 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Using formal algebra....

\n" ); document.write( "let x = # of quarters
\n" ); document.write( "then x+5 = # of half dollars

\n" ); document.write( "The total value is $32.50, or 3250 cents:

\n" ); document.write( " $\"25x+%2B+50%28x%2B5%29+=+32.50\"$

\n" ); document.write( "Solve using basic algebra; I leave that much to you.

\n" ); document.write( "An informal solution using logical reasoning and easy mental arithmetic can get you to the solution faster then the formal algebra, and using very nearly the same steps.

\n" ); document.write( "(1) Count the \"extra\" five half dollars first. That's $2.50, or 250 cents; and it leaves equal numbers of quarters and half dollars with a total value of $30, or 3000 cents.
\n" ); document.write( "(2) Consider groups of one quarter and one half dollar; the value of each group is 75 cents.
\n" ); document.write( "(3) To make the remaining 3000 cents, the number of those groups needs to be 3000/75 = 40.
\n" ); document.write( "(4) So there are 40 quarters and 40+5=45 half dollars.

\n" ); document.write( "Of course the answer you got using formal algebra should be the same.

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