document.write( "Question 1023790: Marvin sold his bike for $20 more than one-third of what he paid for it. He sold it for $70. How much did he pay for it? \n" ); document.write( "

Algebra.Com's Answer #639223 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Use a substitution,
\n" ); document.write( " $\"X=a-b\"$
\n" ); document.write( " $\"Y=a%2Bb\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"%28a-b%29%2F%28a%2Bb%29-%28a%2Bb%29%2F%28a-b%29=X%2FY-Y%2FX\"$
\n" ); document.write( "You want a common denominator $\"XY\"$
\n" ); document.write( "

\r
\n" ); document.write( "\n" ); document.write( " $\"%28a-b%29%2F%28a%2Bb%29-%28a%2Bb%29%2F%28a-b%29=X%5E2%2F%28XY%29-Y%5E2%2F%28XY%29\"$
\n" ); document.write( " $\"%28a-b%29%2F%28a%2Bb%29-%28a%2Bb%29%2F%28a-b%29=%28X%5E2-Y%5E2%29%2F%28XY%29\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"X%5E2=%28a-b%29%5E2=a%5E2-2ab%2Bb%5E2\"$
\n" ); document.write( " $\"Y%5E2=%28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2\"$
\n" ); document.write( " $\"X%5E2-Y%5E2=a%5E2-2ab%2Bb%5E2-a%5E2-2ab-b%5E2\"$
\n" ); document.write( " $\"X%5E2-Y%5E2=-4ab\"$
\n" ); document.write( "and
\n" ); document.write( " $\"XY=%28a-b%29%28a%2Bb%29=a%5E2-b%5E2\"$
\n" ); document.write( "Substituting,
\n" ); document.write( " $\"%28a-b%29%2F%28a%2Bb%29-%28a%2Bb%29%2F%28a-b%29=%28-4ab%29%2F%28a%5E2-b%5E2%29\"$ \n" ); document.write( "

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