document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=301362>Question 301362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A vending machine sells chips at $0.40 and candy at $0.50. Last month, the vending machine yielded $139.80 with the sale of 298 items.\r<BR>\n" );
document.write( "\n" );
document.write( "let x be the number of chips sold and y the number of candies. How many packages of chips were purchased last month? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #216061 by </B><A HREF=/tutors/aboutme.mpl?userid=lukechalfant><B>lukechalfant(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lukechalfant><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=216061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve this one use a system of equations.<BR>\n" );
document.write( "First, you know that the total number of items sold was 298.\r<BR>\n" );
document.write( "\n" );
document.write( "If x is the number of chips and y is the number of candies, then:<BR>\n" );
document.write( "x + y = 298\r<BR>\n" );
document.write( "\n" );
document.write( "Now, you don't know how many chips were sold but you know their cost: $0.40<BR>\n" );
document.write( "If x is the number of chips sold than .4(x) = the total sales of chips.<BR>\n" );
document.write( "Do this with the candy as well: .5(y)<BR>\n" );
document.write( "You also know that the total profit was $139.80. So:<BR>\n" );
document.write( ".4(x) + .5(y) = 139.8 <BR>\n" );
document.write( "(it makes it easier for me to drop off the zeros, you can keep them on if you want to)<BR>\n" );
document.write( "Now multiply the second equation by 10 to get rid of decimals.\r<BR>\n" );
document.write( "\n" );
document.write( "So here are the two equations:<BR>\n" );
document.write( "x + y = 298<BR>\n" );
document.write( "4(x) + 5(y) = 1398\r<BR>\n" );
document.write( "\n" );
document.write( "To solve this there are a few ways. I can't remember the name of this method but the general idea is to make one variable opposite in one equation of what it is in the other. Like 4x and -4x. To get the first equation to have a -4x multiply the entire equation by -4. Then use this with the other equation to cancel out x. Think of it vertically in columns and simplify down, like this:\r<BR>\n" );
document.write( "\n" );
document.write( "-4x + -4y = -1192<BR>\n" );
document.write( " 4x +  5y =  1398<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( " 0x +   y =  206\r<BR>\n" );
document.write( "\n" );
document.write( "So y = 206\r<BR>\n" );
document.write( "\n" );
document.write( "Going back to one of the first equations and plugging in the new found y you get:\r<BR>\n" );
document.write( "\n" );
document.write( "x + 206 = 298<BR>\n" );
document.write( "  - 206  -206\r<BR>\n" );
document.write( "\n" );
document.write( "x = 92\r<BR>\n" );
document.write( "\n" );
document.write( "So they sold 206 candies and 92 bags of chips.\r<BR>\n" );
document.write( "\n" );
document.write( "To check, does 206 + 92 = 298? It does. Does 4(92) + 5(206) = 1398? It does.\r<BR>\n" );
document.write( "\n" );
document.write( "92 bags of chips is the answer. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );