document.write( "Question 1043064: On Monday 30 girls and zero boys in Crescent Valley band missed practice resulting in a 2 to 5 ratio of girls to boys on Tuesday 30 girls and 40 boys miss practice resulting in a 2 to 1 ratio of girls to boys how many students are in the band \n" ); document.write( "

Algebra.Com's Answer #658161 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+b+\"$ = number of boys in the band
\n" ); document.write( "Let $\"+g+\"$ = number of girls in the band
\n" ); document.write( "----------------------------------
\n" ); document.write( "On monday:
\n" ); document.write( "(1) $\"+%28+g+-+30+%29+%2F+b+=+2%2F5+\"$
\n" ); document.write( "On tuesday:
\n" ); document.write( "(2) $\"+%28+g+-+30+%29+%2F+%28+b+-+40+%29+=+2%2F1+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "There are 2 equations and 2 unknowns, so it's solvable
\n" ); document.write( "Multiply both sides of (1) by $\"+5b+\"$
\n" ); document.write( "(1) $\"+5%2A%28+g+-+30+%29+=+2b+\"$
\n" ); document.write( "(1) $\"+5g+-+150+=+2b+\"$
\n" ); document.write( "(1) $\"+5g+-+2b+=+150+\"$
\n" ); document.write( "and
\n" ); document.write( "Multiply both sides of (2) by $\"+b+-+40+\"$
\n" ); document.write( "(2) $\"+g+-+30+=+2%2A%28+b+-+40+%29+\"$
\n" ); document.write( "(2) $\"+g+-+30+=+2b+-+80+\"$
\n" ); document.write( "(2) $\"+-g+%2B+2b+=+50+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "Add (1) and (2)
\n" ); document.write( "(2) $\"+-g+%2B+2b+=+50+\"$
\n" ); document.write( "(1) $\"+5g+-+2b+=+150+\"$
\n" ); document.write( "--------------------
\n" ); document.write( " $\"+4g+=+200+\"$
\n" ); document.write( " $\"+g+=+50+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+-g+%2B+2b+=+50+\"$
\n" ); document.write( "(2) $\"+-50+%2B+2b+=+50+\"$
\n" ); document.write( "(2) $\"+2b+=+100+\"$
\n" ); document.write( "(2) $\"+b+=+50+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "100 students ( 50 girls and 50 boys ) are in the band
\n" ); document.write( "-----------------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+%28+g+-+30+%29+%2F+b+=+2%2F5+\"$
\n" ); document.write( "(1) $\"+%28+50+-+30+%29+%2F+50+=+2%2F5+\"$
\n" ); document.write( "(1) $\"+20%2F50+=+2%2F5+\"$
\n" ); document.write( "OK
\n" ); document.write( "(2) $\"+%28+g+-+30+%29+%2F+%28+b+-+40+%29+=+2%2F1+\"$
\n" ); document.write( "(2) $\"+%28+50+-+30+%29+%2F+%28+50+-+40+%29+=+2%2F1+\"$
\n" ); document.write( "(2) $\"+20+%2F+10+=+2%2F1+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );