document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083064>Question 1083064</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am not a student, but I need to solve a problem related to the cost of an activity; sadly, my receipt does not break down the cost per person.  Total amount paid is $4642.00 for tickets for 5 adults and 1 youth.  The youth ticket price is discounted 20% off the adult ticket price.\r<BR>\n" );
document.write( "\n" );
document.write( "I think the problem is:<BR>\n" );
document.write( "5x + (x - 20%) = 4642\r<BR>\n" );
document.write( "\n" );
document.write( "However, it has been approximately 35 years since I have done algebra and I do not remember how to handle the x - 20% portion of equation.  I need to find the price of an adult for this activity.  I'm not completely sure if this is a one variable equation or 2... HELP!\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697059 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=697059\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have two unknowns: the cost of one adult ticket, and the cost of one youth ticket\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since we have two unknowns, let's make<BR>\n" );
document.write( "x = the cost of one adult ticket<BR>\n" );
document.write( "y = the cost of one youth ticket<BR>\n" );
document.write( "both costs are in dollars\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The fact that \"The youth ticket price is discounted 20% off the adult ticket price\" implies\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "cost of youth ticket = (cost of adult ticket) - (20% of cost of adult ticket)<BR>\n" );
document.write( "y = x - (20% of x)<BR>\n" );
document.write( "y = 1x - 0.2x<BR>\n" );
document.write( "y = (1 - 0.2)x<BR>\n" );
document.write( "y = 0.8x<BR>\n" );
document.write( "So whatever the adult ticket cost is, you take 80% of it to get the youth ticket cost.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We're also given \"Total amount paid is $4642.00 for tickets for 5 adults and 1 youth\", so this means,<BR>\n" );
document.write( "5x+y = 4642.00\r<BR>\n" );
document.write( "\n" );
document.write( "We can replace the 'y' with 0.8x since the two expressions are equal. We now have<BR>\n" );
document.write( "5x+0.8x = 4642.00\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's solve for x<BR>\n" );
document.write( "5x+0.8x = 4642.00<BR>\n" );
document.write( "5.8x = 4642.00<BR>\n" );
document.write( "5.8x/5.8 = 4642.00/5.8<BR>\n" );
document.write( "x = 800.344827586207<BR>\n" );
document.write( "the last value above is approximate. Round this to the nearest penny to get 800.34\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the cost of one adult ticket is roughly $800.34\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The cost of one youth ticket is y = 0.8*x = 0.8*800.34 = 640.272 which rounds to $640.27\r<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "In summary,\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "One adult ticket costs $800.34 <BR>\n" );
document.write( "One youth ticket costs $640.27\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We can check the answer below<BR>\n" );
document.write( "5x+y = 4642.00<BR>\n" );
document.write( "5*800.34+640.27 = 4642.00<BR>\n" );
document.write( "4001.7+640.27 = 4642.00<BR>\n" );
document.write( "4641.97 = 4642.00\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note: due to rounding error, we're off by a few pennies (3 cents to be exact). So I recommend that you make sure you wrote down the proper values. I have a feeling there's a typo somewhere. If not, then it's possible that the rounding error occurred elsewhere.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );