document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82979>Question 82979</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by writing a system of equation.\r<BR>\n" );
document.write( "\n" );
document.write( "a. Anne Matie has 52 coins in dimes and quarters which are worth $6.25. How many of each coin does she have.\r<BR>\n" );
document.write( "\n" );
document.write( "b. John has a total of 9 stamps, which consists of 25 cent and 2 cent stamps. His stamps have a value of $1.10. How many of each stamp does he have?\r<BR>\n" );
document.write( "\n" );
document.write( "c. It takes 4 h for a boat to travel 56 mil downstream. The same boat can 36 mil upstream in 6 hrs. Find the rate of speed of the boat in still water and the rate of the current </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59621 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=59621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve by writing a system of equation.<BR>\n" );
document.write( "a. Anne Matie has 52 coins in dimes and quarters which are worth $6.25. How many of each coin does she have.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The number of coins equation<BR>\n" );
document.write( "d + q = 52<BR>\n" );
document.write( "d = 52-q; use for substitution<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The $amt equation:<BR>\n" );
document.write( ".10d + .25q = 6.25<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Substitute (52-q) for d in the above equation:<BR>\n" );
document.write( ".10(52-q) + .25q = 6.25<BR>\n" );
document.write( "5.2 - .10q + .25q = 6.25<BR>\n" );
document.write( "+.15q = 6.25 - 5.2<BR>\n" );
document.write( ".15q = 1.05<BR>\n" );
document.write( "q = 1.05/.15<BR>\n" );
document.write( "q = 7 quarters<BR>\n" );
document.write( "and<BR>\n" );
document.write( "d = 52 -7 = 45 dimes<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check .10(45) + .25(7) = 6.25<BR>\n" );
document.write( ": <BR>\n" );
document.write( ":<BR>\n" );
document.write( "b. John has a total of 9 stamps, which consists of 25 cent and 2 cent stamps. His stamps have a value of $1.10. How many of each stamp does he have?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = no. of 25 cent stamps<BR>\n" );
document.write( "Then (9-x) = no. of 2 cent stamps<BR>\n" );
document.write( ":<BR>\n" );
document.write( ".25x + .02(9-x) = 1.10<BR>\n" );
document.write( ".25x + .18 - .02x = 1.10<BR>\n" );
document.write( ".23x = 1.10 - .18<BR>\n" );
document.write( ".23x = .92<BR>\n" );
document.write( "x = .92/.23<BR>\n" );
document.write( "x = 4 ea 25 cent stamps<BR>\n" );
document.write( "Obviously that leave 5 ea 2 cent stamps<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Check solution:<BR>\n" );
document.write( ".25(4) + .02(5) = 1.10<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "c. It takes 4 h for a boat to travel 56 mil downstream. The same boat can 36 mil upstream in 6 hrs. Find the rate of speed of the boat in still water and the rate of the current<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = speed of the boat in still water; Let y = speed of the current:<BR>\n" );
document.write( "Then:<BR>\n" );
document.write( "Speed upstream: (x-y)<BR>\n" );
document.write( "Speed downstream: (x+y)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write two distance equations; dist = time * speed<BR>\n" );
document.write( "4(x + y) = 56<BR>\n" );
document.write( "6(x - y) = 36<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Divide the 1st equation by 4 and the 2nd equation by 6 and you have:<BR>\n" );
document.write( "x + y = 14<BR>\n" );
document.write( "x - y =  6<BR>\n" );
document.write( "-------------adding eliminates y; find x<BR>\n" );
document.write( "2x + 0 = 20<BR>\n" );
document.write( "x = 20/2<BR>\n" );
document.write( "x = 10 mph in still water<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find y using x - y = 6<BR>\n" );
document.write( "10 - y = 6<BR>\n" );
document.write( "y = 4 mph is the current<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solutions:<BR>\n" );
document.write( "4(10+4) = 52<BR>\n" );
document.write( "6(10-4) = 36 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );