document.write( "Question 434946: Bertha has 33 coins in her pocket totaling $5.25. If she only has nickles and quarters, how many of each type of coin does she have \n" ); document.write( "

Algebra.Com's Answer #853271 by greenestamps(13276) $\"\"$ $\"About$

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\n" ); document.write( "The formal algebraic solutions shown by the other tutors are fine.

\n" ); document.write( "The problem can be solved informally using logical reasoning and mental arithmetic. If your mental arithmetic is good, this can be faster than using formal algebra. That can be helpful in some case, such as a timed competitive exam.

\n" ); document.write( "Solving problems informally can also provide excellent brain exercise.

\n" ); document.write( "Here is an informal solution to the problem.

\n" ); document.write( "(1) If all 33 coins were nickels, the total would be 33(5) = 165 cents, or $1.65. The actual total, $5.25, or 525 cents, is 525-165 = 360 cents more.
\n" ); document.write( "(2) Each quarter is worth 25-5 = 20 cents more than each nickel.
\n" ); document.write( "(3) The number of quarters needed to make the additional 360 cents is 360/20 = 18.

\n" ); document.write( "So there are 18 quarters and 33-18 = 15 nickels.

\n" ); document.write( "ANSWER: 18 quarters, 15 nickels

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