document.write( "Question 533419: I have a math problem that say this: Constance has $2.80 in quarters and dimes. The number of quarters exceeds three times the number of dimes by 1. Find the number she has of each kind. What do they mean by 1? \n" ); document.write( "

Algebra.Com's Answer #351061 by josmiceli(19441) $\"\"$ $\"About$

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They mean that she has 3 times as many quarters as dimes
\n" ); document.write( "plus 1 more quarter.
\n" ); document.write( "For example, if she had 5 dimes, then she would have
\n" ); document.write( " $\"+3%2A5+\"$ = 15 quarters plus 1 more quarter = 16 quarters
\n" ); document.write( "----------------
\n" ); document.write( "As for your problem,
\n" ); document.write( "Let $\"q\"$ = number of quarters she has
\n" ); document.write( "Let $\"d\"$ = number of dimes she has
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+q+=+3d+%2B+1+\"$
\n" ); document.write( "(2) $\"+25q+%2B+10d+=+280+\"$ ( in cents )
\n" ); document.write( "---------------------
\n" ); document.write( "Divide both sides of (2) by $\"5\"$
\n" ); document.write( "(2) $\"+5q+%2B+2d+=+56+\"$
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+5%2A%28+3d+%2B+1+%29+%2B+2d+=+56+\"$
\n" ); document.write( "(2) $\"+15d+%2B+5+%2B+2d+=+56+\"$
\n" ); document.write( "(2) $\"+17d+=+51+\"$
\n" ); document.write( "(2) $\"+d+=+3+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+q+=+3d+%2B+1+\"$
\n" ); document.write( "(1) $\"+q+=+3%2A3+%2B+1+\"$
\n" ); document.write( "(1) $\"+q+=+10+\"$
\n" ); document.write( "She has 10 quarters and 3 dimes \n" ); document.write( "

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