document.write( "Question 1088907: a coin jar has 50coins consisting of nickels, dimes, and quarters. The total value of the coins in the jar is $5.75. How many nickels, dimes, quarters are in the jar ? \n" ); document.write( "

Algebra.Com's Answer #703227 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+n+\"$ = the number of nickels
\n" ); document.write( "Let $\"+d+\"$ = the number of dimes
\n" ); document.write( "Let $\"+q+\"$ = the number of quarters
\n" ); document.write( "------------------------------------
\n" ); document.write( "(1) $\"+n+%2B+d+%2B+q+=+50+\"$
\n" ); document.write( "(2) $\"+5n+%2B+10d+%2B+25q+=+575+\"$
\n" ); document.write( "---------------------------------
\n" ); document.write( "The are 3 unknowns but only 2 equations,
\n" ); document.write( "so this is not directly solvable, but still
\n" ); document.write( "can be analyzed. There may be several solutions
\n" ); document.write( "-------------------------
\n" ); document.write( "Thee must be less than 23 quarters, since
\n" ); document.write( " $\"+23%2A25+=+575+\"$
\n" ); document.write( "-------------------
\n" ); document.write( " $\"+n+%2B+d+%3C+50+-+23+\"$
\n" ); document.write( " $\"+n+%2B+d+%3C+27+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "Suppose ther are 20 quarters
\n" ); document.write( " $\"+20%2A25+=+500+\"$
\n" ); document.write( "Suppose there are 9 nickels
\n" ); document.write( " $\"+9%2A5+=+45+\"$
\n" ); document.write( "and 3 dimes
\n" ); document.write( " $\"+3%2A10+=+30+\"$
\n" ); document.write( " $\"+500+%2B+45+%2B+30+=+575+\"$ but
\n" ); document.write( " $\"+20+%2B+9+%2B+3+=+32+\"$
\n" ); document.write( "so, there are too many quarters
\n" ); document.write( "------------------------------
\n" ); document.write( "Let $\"+q+=+15+\"$
\n" ); document.write( " $\"+15%2A25+=+375+\"$
\n" ); document.write( "Let $\"+n+=+18+\"$
\n" ); document.write( " $\"+18%2A5+=+90+\"$
\n" ); document.write( "Let $\"+d+=+11+\"$
\n" ); document.write( " $\"+11%2A10+=+110+\"$
\n" ); document.write( " $\"+375+%2B+90+%2B+110+=+575+\"$ but
\n" ); document.write( " $\"+15+%2B+18+%2B+11+=+44+\"$
\n" ); document.write( "--------------------------------
\n" ); document.write( "Closer, but I still have too many quarters
\n" ); document.write( "Let $\"+q+=+13+\"$
\n" ); document.write( " $\"+13%2A25+=+325+\"$
\n" ); document.write( "Let $\"+n+=+20+\"$
\n" ); document.write( " $\"+20%2A5+=+100+\"$
\n" ); document.write( "Let $\"+d+=+15+\"$
\n" ); document.write( " $\"+15%2A10+=+150+\"$
\n" ); document.write( " $\"+325+%2B+100+%2B+150+=+575+\"$ but
\n" ); document.write( " $\"+13+%2B+20+%2B+15+=+48+\"$ closer
\n" ); document.write( "--------------------------------
\n" ); document.write( " $\"+q+=+13+\"$
\n" ); document.write( " $\"+n+=+22+\"$
\n" ); document.write( " $\"+d+=+15+\"$
\n" ); document.write( " $\"+13%2A25+%2B+22%2A5+%2B+15%2A10+=+325+%2B+110+%2B+150+\"$
\n" ); document.write( " $\"+325+%2B+110+%2B+150+=+585+\"$ too high
\n" ); document.write( "------------------
\n" ); document.write( " $\"+q+=+13+\"$
\n" ); document.write( " $\"+n+=+24+\"$
\n" ); document.write( " $\"+d+=+13+\"$
\n" ); document.write( " $\"+13+%2B+24+%2B+13+=+50+\"$
\n" ); document.write( " $\"+13%2A25+%2B+24%2A5+%2B+13%2A10+=+325+%2B+120+%2B+130+\"$
\n" ); document.write( " $\"+325+%2B+120+%2B+130+=+575+\"$
\n" ); document.write( "BIngo!
\n" ); document.write( "13 quarters
\n" ); document.write( "13 dimes
\n" ); document.write( "24 nickels
\n" ); document.write( "------------------
\n" ); document.write( "There definitely may be other solutions, but this is one of them\r
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