document.write( "Question 999203: In a recent basketball game between the Storm and the Chargers the number of points scored by the Storm in the first half was equal to the number of points scored by the Chargers in the second half of the game. In the first half the Storm scored one-fourth the total points scored in the game. During the second half the Chargers scored 16 points less than one-third the points scored in the game. How many total points were scored during the game? \n" ); document.write( "

Algebra.Com's Answer #616995 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+s%5B1%5D+\"$ = points scored by Storm
\n" ); document.write( "in the 1st half
\n" ); document.write( "Let $\"+c%5B1%5D+\"$ = points scored by Chargers
\n" ); document.write( "in the 1st half
\n" ); document.write( "-------------
\n" ); document.write( "Let $\"+s%5B2%5D+\"$ = points scored by Storm
\n" ); document.write( "in the 2nd half
\n" ); document.write( "Let $\"+c%5B2%5D+\"$ = points scored by Chargers
\n" ); document.write( "in the 2nd half
\n" ); document.write( "--------------
\n" ); document.write( "(1) $\"+s%5B1%5D+=+c%5B2%5D+\"$
\n" ); document.write( "(2) $\"+s%5B1%5D+=+%281%2F4%29%2A%28+s%5B1%5D+%2B+c%5B1%5D+%2B+s%5B2%5D+%2B+c%5B2%5D+%29+\"$
\n" ); document.write( "(3) $\"+c%5B2%5D+=+%281%2F3%29%2A%28+s%5B1%5D+%2B+c%5B1%5D+%2B+s%5B2%5D+%2B+c%5B2%5D+%29+-+16+\"$
\n" ); document.write( "-----------------------------------------
\n" ); document.write( "(3) $\"+s%5B1%5D+%2B+c%5B1%5D+%2B+s%5B2%5D+%2B+c%5B2%5D+=+3%2A%28+c%5B2%5D+%2B+16+%29+\"$
\n" ); document.write( "(2) $\"+s%5B1%5D+%2B+c%5B1%5D+%2B+s%5B2%5D+%2B+c%5B2%5D+=+4%2As%5B1%5D+\"$
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+s%5B1%5D+%2B+c%5B1%5D+%2B+s%5B2%5D+%2B+c%5B2%5D+=+4%2Ac%5B2%5D+\"$
\n" ); document.write( "(3) $\"+4%2Ac%5B2%5D+=+3%2A%28+c%5B2%5D+%2B+16+%29+\"$
\n" ); document.write( "(3) $\"+4c%5B2%5D+-+3c%5B2%5D+=+48+\"$
\n" ); document.write( "(3) $\"+c%5B2%5D+=+48+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+s%5B1%5D+=+48+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "Now I can say:
\n" ); document.write( "(2) $\"+s%5B1%5D+%2B+c%5B1%5D+%2B+s%5B2%5D+%2B+c%5B2%5D+=+4%2Ac%5B2%5D+\"$
\n" ); document.write( "(2) $\"+48+%2B+c%5B1%5D+%2B+s%5B2%5D+%2B+48+=+4%2A48+\"$
\n" ); document.write( "(2) $\"+c%5B1%5D+%2B+s%5B2%5D+=+2%2A48+\"$
\n" ); document.write( "(2) $\"+c%5B1%5D+%2B+s%5B2%5D+=+96+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "The total number of points in the game were:
\n" ); document.write( " $\"+s%5B1%5D+%2B+c%5B1%5D+%2B+s%5B2%5D+%2B+c%5B2%5D+=+4%2A48+\"$
\n" ); document.write( " $\"+s%5B1%5D+%2B+c%5B1%5D+%2B+s%5B2%5D+%2B+c%5B2%5D+=+192+\"$
\n" ); document.write( "192 points were scored in the game \n" ); document.write( "

\n" );