document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1036234>Question 1036234</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #650875 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=650875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of hits<BR>\n" );
document.write( "y = number of misses\r<BR>\n" );
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document.write( "He took 29 shots, so the total x+y must be equal to 29. The first equation is therefore\r<BR>\n" );
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document.write( "x+y = 29\r<BR>\n" );
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document.write( "solve for y to get \r<BR>\n" );
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document.write( "y = 29 - x\r<BR>\n" );
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document.write( "The game pays 7 cents for each hit. Chuck made x hits. So he receives 7*x cents, where x is some positive whole number. Keep this fact in mind: x cannot be some fractional or decimal value. It must be a positive whole number. \r<BR>\n" );
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document.write( "Chuck loses 5 cents for each miss. If he missed y times (y is a positive whole number) then he lost 5*y cents. A loss in mathematics is often denoted with a negative number. For instance, if you lost 5 dollars, then you'd record it in a ledger with the value -5.\r<BR>\n" );
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document.write( "Since he gains 7*x cents for the x hits and loses 5*y cents for the y losses, this means we have\r<BR>\n" );
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document.write( "7*x + (-5*y) = 7x - 5y\r<BR>\n" );
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document.write( "The expression 7x - 5y is then set equal to -37 to indicate he lost a net of 37 cents. After the gains and losses are totaled, at the end of the day, he lost 37 cents total. \r<BR>\n" );
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document.write( "So that means we have this second equation\r<BR>\n" );
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document.write( "7x - 5y = -37\r<BR>\n" );
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document.write( "Let's plug y = 29 - x into the second equation and see what we get when we solve for x.\r<BR>\n" );
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document.write( "7x - 5y = -37<BR>\n" );
document.write( "7x - 5(29 - x) = -37<BR>\n" );
document.write( "7x - 145 + 5x = -37<BR>\n" );
document.write( "12x - 145 = -37<BR>\n" );
document.write( "12x - 145+145 = -37+145<BR>\n" );
document.write( "12x = 108<BR>\n" );
document.write( "12x/12 = 108/12<BR>\n" );
document.write( "x = 9\r<BR>\n" );
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document.write( "So Chuck got 9 hits. Use this value of x to get the value of y\r<BR>\n" );
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document.write( "y = 29 - x<BR>\n" );
document.write( "y = 29 - 9<BR>\n" );
document.write( "y = 20\r<BR>\n" );
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document.write( "which means he got 20 misses.\r<BR>\n" );
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document.write( "Final Answer: Chuck got 9 hits and 20 misses<BR>\n" );
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