document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210397>Question 1210397</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Andrew bought some apples and pears. The ratio of the number of apples bought to the number of pears bought was 7:4. He spent $61.20. He paid $22.80 more for the apples than the pears. Each apple was $0.30 more than each pears.<BR>\n" );
document.write( "(a) How much did he spend on the pears?<BR>\n" );
document.write( "(b) How many pears did he buy? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852209 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=852209\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There are many ways you could set up this problem for solving.  I looked briefly at a few different ways before choosing a method that looked as if it would be relatively easy.  I would hope that other tutors might come to you with different solutions.<br><BR>\n" );
document.write( "He spent a total of $61.20; and he spent $22.80 more for the apples than for the pears.<br><BR>\n" );
document.write( "let a = cost of the apples<BR>\n" );
document.write( "let p = cost of the pears<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bp=61.20 ALIGN=MIDDLE  ALT=\"a%2Bp=61.20\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the total cost was $61.20<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-p=22.80 ALIGN=MIDDLE  ALT=\"a-p=22.80\"   DISABLED_style= \"max-width:90%; height:auto;\" >  the cost of the apples was $22.80 more than the cost of the pears<br><BR>\n" );
document.write( "Solve the pair of equations by adding the two equations to solve for a and then use that number to find p.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a=84.00 ALIGN=MIDDLE  ALT=\"2a=84.00\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=42.00 ALIGN=MIDDLE  ALT=\"a=42.00\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=42.00-22.80=19.20 ALIGN=MIDDLE  ALT=\"p=42.00-22.80=19.20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The total cost of the apples was $42; the total cost of the pears was $19.20.<br><BR>\n" );
document.write( "The ratio of the number of apples to the number of pears was 7:4.  So<br><BR>\n" );
document.write( "let 7x = number of apples<BR>\n" );
document.write( "then 4x = number of pears<br><BR>\n" );
document.write( "Find the cost of x apples and the cost of x pears:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x=42 ALIGN=MIDDLE  ALT=\"7x=42\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The cost of x apples is $6.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=19.20 ALIGN=MIDDLE  ALT=\"4x=19.20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4.80 ALIGN=MIDDLE  ALT=\"x=4.80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The cost of x pears is $4.80.<br><BR>\n" );
document.write( "The cost of x apples is $6 - $4.80 = $1.20 more than the cost of x pears.  Each apple costs $0.30 more than each pear, so x = $1.20/$0.30 = 4.<br><BR>\n" );
document.write( "The cost of x=4 apples is $6, so the cost of each apple is $6/4 = $1.50.<br><BR>\n" );
document.write( "The cost of x=4 pears is $4.80, so the cost of each pear is $4.80/4 = $1.20.<br><BR>\n" );
document.write( "Check the results we have with the original given information:<br><BR>\n" );
document.write( "He bought 7x = 28 apples at $1.50 each for a total of 28($1.50) = $42.00.<BR>\n" );
document.write( "He bought 4x = 16 pears at $1.20 each for a total of 16($1.20) = $19.20.<BR>\n" );
document.write( "The total he spent was $42.00+$19.20 = $61.20.<br><BR>\n" );
document.write( "Looks good.  Now answer the questions that were asked.<br><BR>\n" );
document.write( "(a) How much did he spend on the pears?<BR>\n" );
document.write( "ANSWER: $19.20<br><BR>\n" );
document.write( "(b) How many pears did he buy?<BR>\n" );
document.write( "ANSWER: 16<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );