document.write( "Question 1036234: A game pays 7 cents for a hit and charges 5 cents for a miss. Chuck took 29 shots and lost 37 cents. How many hits and how many misses did he have? set up equation using 2 variables. \n" ); document.write( "
Algebra.Com's Answer #650874 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let the number of hits be x\r\n" );
document.write( "Let the number of misses be y\r\n" );
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document.write( "                      Value      Value\r\n" );
document.write( "Type       Number       of         of\r\n" );
document.write( " of          of        EACH       ALL\r\n" );
document.write( "shot        shots      shot      shots\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "hits         x       $0.07       $0.07x\r\n" );
document.write( "misses       y      -$0.05      -$0.05y\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS      29       -----      -$0.37\r\n" );
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document.write( " The first equation comes from the \"Number of shots\" column.\r\n" );
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document.write( "  \"%28matrix%283%2C1%2CNumber%2Cof%2Chits%29%29\"\"%22%22%2B%22%22\"\"%28matrix%283%2C1%2CNumber%2Cof%2Cmisses%29%29\"\"%22%22=%22%22\"\"%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Cshots%29%29\"\r\n" );
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document.write( "                     x + y = 29\r\n" );
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document.write( " The second equation comes from the \"Value of all shots\" column.\r\n" );
document.write( "  \"%28matrix%284%2C1%2CValue%2Cof%2CALL%2Chits%29%29\"\"%22%22%2B%22%22\"\"%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cmisses%29%29\"\"%22%22=%22%22\"\"%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Cshots%29%29\"\r\n" );
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document.write( "            0.07x - 0.05y = -0.37\r\n" );
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document.write( "Get rid of decimals by multiplying every term by 100:\r\n" );
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document.write( "                 7x + -5y = -37\r\n" );
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document.write( " So we have the system of equations:\r\n" );
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document.write( "           \"system%28x+%2B+y+=+29%2C7x+%2B+-5y+=+-37%29\".\r\n" );
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document.write( "We solve by substitution.  Solve the first equation for y:\r\n" );
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document.write( "                                x + y = 29\r\n" );
document.write( "                                    y = 29 - x\r\n" );
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document.write( "Substitute (29 - x) for y in 7x + -5y = -37\r\n" );
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document.write( "                       7x - 5(29 - x) = -37\r\n" );
document.write( "                        7x - 145 + 5x = -37\r\n" );
document.write( "                           12x + -145 = -37\r\n" );
document.write( "                                  12x = 108\r\n" );
document.write( "                                    x = 9 = the number of hits.\r\n" );
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document.write( "                      Substitute in y = 29 - x\r\n" );
document.write( "                                    y = 29 - (9)\r\n" );
document.write( "                                    y = 20 misses.\r\n" );
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document.write( "Checking:  9 hits is $0.63 and 20 miss is -$1.00\r\n" );
document.write( "            That's 29 shots.\r\n" );
document.write( "            And indeed $0.63 - $1.00 = -$0.37\r\n" );
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document.write( "Edwin
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