document.write( "Question 1012706: Anna scored 646 points making 355 shots, including 3-point field goals, 2-point field goals, and 1-point free throws. She made 27 more 2-point field goals than 3-point field goals. Write a system of three equations that represents the number of goals Anna made\r
\n" ); document.write( "\n" ); document.write( "Find the number of each type of goal she made for
\n" ); document.write( "3-point goals
\n" ); document.write( "2-point goals
\n" ); document.write( "1-point free throws \n" ); document.write( "

Algebra.Com's Answer #628739 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+a+\"$ =number of 1-point shots
\n" ); document.write( "Let $\"+b+\"$ =number of 2-point shots
\n" ); document.write( "Let $\"+c+\"$ =number of 3-point shots
\n" ); document.write( "---------------------------------
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+355+\"$
\n" ); document.write( "(2) $\"+1%2Aa+%2B+2%2Ab+%2B+3%2Ac+=+646+\"$
\n" ); document.write( "(3) $\"+b+=+c+%2B+27+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( "This is 3 equations and 3 unknowns,
\n" ); document.write( "so it is solvable
\n" ); document.write( "-------------------
\n" ); document.write( "Substitute (3) into (2)
\n" ); document.write( "(2) $\"+1%2Aa+%2B+2%2A%28+c+%2B+27+%29+%2B+3%2Ac+=+646+\"$
\n" ); document.write( "(2) $\"+a+%2B+2c+%2B+54+%2B+3c+=+646+\"$
\n" ); document.write( "(2) $\"+a+%2B+5c+=+592+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "Substitute (3) into (1)
\n" ); document.write( "(1) $\"+a+%2Bc+%2B+27+%2B+c+=+355+\"$
\n" ); document.write( "(1) $\"+a+%2B+2c+=+328+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "(2) $\"+a+%2B+5c+=+592+\"$
\n" ); document.write( "(1) $\"+-a+-+2c+=+-328+\"$
\n" ); document.write( "--------------------
\n" ); document.write( " $\"+3c+=+264+\"$
\n" ); document.write( " $\"+c+=+88+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+b+=+c+%2B+27+\"$
\n" ); document.write( "(3) $\"+b+=+88+%2B+27+\"$
\n" ); document.write( "(3) $\"+b+=+115+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+355+\"$
\n" ); document.write( "(1) $\"+a+%2B+115+%2B+88+=+355+\"$
\n" ); document.write( "(1) $\"+a+=+355+-+203+\"$
\n" ); document.write( "(1) $\"+a+=+152+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "88 3-point goals
\n" ); document.write( "115 2-point goals
\n" ); document.write( "152 1-point free throws
\n" ); document.write( "-----------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+1%2Aa+%2B+2%2Ab+%2B+3%2Ac+=+646+\"$
\n" ); document.write( "(2) $\"+1%2A152+%2B+2%2A115+%2B+3%2A88+=+646+\"$
\n" ); document.write( "(2) $\"+152+%2B+230+%2B+264+=+646+\"$
\n" ); document.write( "(2) $\"+646+=+646+\"$
\n" ); document.write( "You can check other 2 equations \n" ); document.write( "

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