document.write( "Question 227432: Brian O'Reilly earns twice as much each week as a tutor than he does pumping gas. His total weekly wages are $150 more than that of his younger sister. She earns one quarter as much as Brian does as a tutor. How much does Brian earn as a tutor? \n" ); document.write( "

Algebra.Com's Answer #169013 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"t\"$ = Brian's weekly earnings as a tutor
\n" ); document.write( "Let $\"g\"$ = Brian's weekly earnings pumping gas
\n" ); document.write( "LKet $\"s\"$ = Sister's weekly earnings
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"t+=+2g\"$
\n" ); document.write( "(2) $\"t+%2B+g+=+s+%2B+150\"$
\n" ); document.write( "(3) $\"s+=+%281%2F4%29%2At\"$
\n" ); document.write( "This is 3 equations and 3 unknowns, so it's solvable
\n" ); document.write( "First, substitute (3) in (2)
\n" ); document.write( "(2) $\"t+%2B+g+=+s+%2B+150\"$
\n" ); document.write( "(2) $\"t+%2B+g+=+%281%2F4%29%2At+%2B+150\"$
\n" ); document.write( "Now solve (1) for $\"g\"$ and substitute in (2)
\n" ); document.write( "(1) $\"t+=+2g\"$
\n" ); document.write( " $\"g+=+t%2F2\"$
\n" ); document.write( "(2) $\"t+%2B+g+=+%281%2F4%29%2At+%2B+150\"$
\n" ); document.write( " $\"t+%2B+t%2F2+=+t%2F4+%2B+150\"$
\n" ); document.write( " $\"t+%2B+t%2F4+=+150\"$
\n" ); document.write( " $\"1.25t+=+150\"$
\n" ); document.write( " $\"t+=+120\"$
\n" ); document.write( "and, from (1)
\n" ); document.write( " $\"g+=+t%2F2\"$
\n" ); document.write( " $\"g+=+60\"$
\n" ); document.write( "and, from (3)
\n" ); document.write( " $\"s+=+t%2F4\"$
\n" ); document.write( " $\"s+=+30\"$
\n" ); document.write( "Brian earns $120/wk as a tutor
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"t+%2B+g+=+s+%2B+150\"$
\n" ); document.write( "(2) $\"120+%2B+60+=+30+%2B+150\"$
\n" ); document.write( " $\"180+=+180\"$
\n" ); document.write( "OK \n" ); document.write( "

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