document.write( "Question 676981: Please help me solve this word problem- While playing basketball, Mr. Koster scored 32 points. Points came from a combination of free throws, 2-pointers and 3-pointers. He made 19 baskets in total with half as many 2-pointers as free throws. How many of each type of basket did he make? \n" ); document.write( "

Algebra.Com's Answer #420634 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = number of free throws
\n" ); document.write( "Let $\"+b+\"$ = number of 2-pointers
\n" ); document.write( "Let $\"+c+\"$ = number of 3-pointers
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+19+\"$
\n" ); document.write( "(2) $\"+a+%2B+2b+%2B+3c+=+32+\"$
\n" ); document.write( "(3) $\"+a+=+2b+\"$
\n" ); document.write( "---------------
\n" ); document.write( "Substitute (3) into (1)
\n" ); document.write( "(1) $\"+2b+%2B+b+%2B+c+=+19+\"$
\n" ); document.write( "(1) $\"+c+=+19+-+3b+\"$
\n" ); document.write( "Substitute (1) and (3) into (2)
\n" ); document.write( "(2) $\"+a+%2B+2b+%2B+3c+=+32+\"$
\n" ); document.write( "(2) $\"+2b+%2B+2b+%2B+3%2A%28+19+-+3b+%29+=+32+\"$
\n" ); document.write( "(2) $\"+4b+%2B+57+-+9b+=+32+\"$
\n" ); document.write( "(2) $\"+5b+=+57+-+32+\"$
\n" ); document.write( "(2) $\"+5b+=+25+\"$
\n" ); document.write( "(2) $\"+b+=+5+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+c+=+19+-+3b+\"$
\n" ); document.write( "(1) $\"+c+=+19+-+3%2A5+\"$
\n" ); document.write( "(1) $\"+c+=+4+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+a+=+2b+\"$
\n" ); document.write( "(3) $\"+a+=+2%2A5+\"$
\n" ); document.write( "(3) $\"+a+=+10+\"$
\n" ); document.write( "The number of free throws is 10
\n" ); document.write( "The number of 2-pointers is 5
\n" ); document.write( "The number of 3-pointers is 4
\n" ); document.write( "---------------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+a+%2B+2b+%2B+3c+=+32+\"$
\n" ); document.write( "(2) $\"+10+%2B+2%2A5+%2B+3%2A4+=+32+\"$
\n" ); document.write( "(2) $\"+10+%2B+10+%2B+12+=+32+\"$
\n" ); document.write( "(2) $\"+32+=+32+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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