document.write( "Question 1029239: marnie has 18 coins in the ratio of 1 dollar and 2 quarter. what coins does she spend to give a new ratio of dollars to quarters of 1:3? Give all possible answers. \n" ); document.write( "

Algebra.Com's Answer #644300 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
There are twice as many quarters as dollars
\n" ); document.write( "Let $\"+d+\"$ = number of dollars
\n" ); document.write( " $\"+d+%2B+2d+=+18+\"$
\n" ); document.write( " $\"+3d+=+18+\"$
\n" ); document.write( " $\"+d+=+6+\"$
\n" ); document.write( "There are $\"+18+-+6+=+12+\"$ quarters
\n" ); document.write( "-------------
\n" ); document.write( "The only way to spend and get the ratio
\n" ); document.write( " $\"+d%2Fq+=+1%2F2+\"$ down to $\"+d%2Fq+=+1%2F3+\"$
\n" ); document.write( "is to spend dollars or both dollars and quarters
\n" ); document.write( "------------------
\n" ); document.write( "I can say:
\n" ); document.write( " $\"+%28+6+-+x+%29+%2F+12+=+1%2F3+\"$
\n" ); document.write( "Multiply both sides by $\"+12+\"$
\n" ); document.write( " $\"+6+-+x+=+4+\"$
\n" ); document.write( " $\"+x+=+2+\"$
\n" ); document.write( "Spend just 2 dollars
\n" ); document.write( "----------------------
\n" ); document.write( "Now I can say:
\n" ); document.write( " $\"+%28+6+-+x+%29+%2F+%28+12+-+y+%29+=+1%2F3+\"$
\n" ); document.write( " $\"+3%2A%28+6+-+x+%29+=+12+-+y+\"$
\n" ); document.write( " $\"+18+-+3x+=+12+-+y+\"$
\n" ); document.write( " $\"+3x+-+y+=+6+\"$
\n" ); document.write( "Any whole number solution is good as
\n" ); document.write( "long as $\"+x+%3C+6+\"$ and $\"+y+%3C+12+\"$
\n" ); document.write( "------------------
\n" ); document.write( " $\"+x+=+4+\"$ and
\n" ); document.write( " $\"+y+=+6+\"$ works
\n" ); document.write( "spend 4 dollars and 6 quarters
\n" ); document.write( "d/q = 2/6
\n" ); document.write( "-----------------------------
\n" ); document.write( " $\"+x+=+5+\"$ and
\n" ); document.write( " $\"+y+=+9+\"$ works
\n" ); document.write( "spend 5 dollars and 9 quarters
\n" ); document.write( "d/q = 1/3
\n" ); document.write( "------------------------------
\n" ); document.write( " $\"+x+=+3+\"$ and
\n" ); document.write( " $\"+y+=+3+\"$ works
\n" ); document.write( "spend 3 dollars and 3 quarters
\n" ); document.write( "d/q = 3/9
\n" ); document.write( "------------------------------
\n" ); document.write( "I think that's it \n" ); document.write( "

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