document.write( "Question 1166932: Lucy has 11 more dimes than pennies. She has $10.12 total. How many of each type of coin does she have? \n" ); document.write( "

Algebra.Com's Answer #791503 by greenestamps(13334) $\"\"$ $\"About$

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\n" ); document.write( "The other tutor has shown one formal algebraic solution.

\n" ); document.write( "I personally prefer to set up problems using a single variable if it is easy to do so.

\n" ); document.write( "Let x be the number of pennies; the number of dimes is then x+11.

\n" ); document.write( "Now we have a single equation to solve, instead of a system of two equations.

\n" ); document.write( " $\"1%28x%29%2B10%28x%2B11%29+=+1012\"$
\n" ); document.write( " $\"x%2B10x%2B110+=+1012\"$
\n" ); document.write( " $\"11x+=+902\"$
\n" ); document.write( " $\"x+=+902%2F11+=+82\"$

\n" ); document.write( "ANSWER: x = 82 pennies and x+11 = 93 dimes

\n" ); document.write( "If your mental arithmetic is good, you can get the answer informally, using virtually the same calculations as above.

\n" ); document.write( "(1) Count the \"extra\" 11 dimes, with a total value of 110 cents.
\n" ); document.write( "(2) the remaining amount, 1012-110 = 902 cents, is made up of equal numbers of pennies and dimes.
\n" ); document.write( "(3) 1 penny and 1 dime together have a value of 11 cents.
\n" ); document.write( "(4) The number of groups at 11 cents each needed to make the remaining 902 cents is 902/11 = 82.
\n" ); document.write( "(5) So there are 82 pennies and 82+11=93 dimes.

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