document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197826>Question 1197826</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "There were 207 pears and 176 mangoes in crate A . There were 293 pears and 274 mango in crate B. Rob moved some pears and mangoes from B to A . In the end 40% of the fruit in A and 70% of the fruit in B were pears. How many pieces of fruit did he move from B to A. Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831245 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=831245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "p = number of pears moved from B to A<BR>\n" );
document.write( "m = number of mangoes moved from B to A<BR>\n" );
document.write( "These variables represent positive whole numbers {1,2,3,...}\r<BR>\n" );
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document.write( "After moving p of the pears and m mangoes from crate B to crate A, we have 207+p pears out of 207+176+p+m = 383+p+m total fruit in crate A.<BR>\n" );
document.write( "The ratio (207+p)/(383+p+m) is set equal to 0.40 since the new percentage of pears in crate A is 40%.\r<BR>\n" );
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document.write( "Let's solve for the variable m.<BR>\n" );
document.write( "(207+p)/(383+p+m) = 0.40 <BR>\n" );
document.write( "207+p = 0.40*383+0.40*p+0.40*m <BR>\n" );
document.write( "207+p = 153.2+0.40p+0.40m<BR>\n" );
document.write( "0.40m = 207+p-153.2-0.40p <BR>\n" );
document.write( "0.40m = 0.6p + 53.8<BR>\n" );
document.write( "m = (0.6p + 53.8)/0.40<BR>\n" );
document.write( "m = (0.6p)/0.40 + (53.8)/0.40<BR>\n" );
document.write( "m = 1.5p + 134.5<BR>\n" );
document.write( "We'll use this in a substitution step later.\r<BR>\n" );
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document.write( "After moving p of the pears and m of the mangoes from B to A we have 293-p pears left in crate B<BR>\n" );
document.write( "This is out of 293+274-p-m = 567-p-m total fruit in crate B.\r<BR>\n" );
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document.write( "We want this ratio<BR>\n" );
document.write( "(293-p)/(567-p-m)<BR>\n" );
document.write( "to be set equal to 0.70 to reflect the fact 70% of the fruit left in crate B are pears.\r<BR>\n" );
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document.write( "So we form this equation<BR>\n" );
document.write( "(293-p)/(567-p-m) = 0.70\r<BR>\n" );
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document.write( "Let's replace m with 1.5p+134.5<BR>\n" );
document.write( "This is what I referred to in the substitution step.<BR>\n" );
document.write( "(293-p)/(567-p-m) = 0.70<BR>\n" );
document.write( "(293-p)/(567-p-(1.5p+134.5)) = 0.70<BR>\n" );
document.write( "(293-p)/(567-p-1.5p-134.5) = 0.70<BR>\n" );
document.write( "(293-p)/(-2.5p+432.5) = 0.70\r<BR>\n" );
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document.write( "We're left with one variable in which we can solve for p.<BR>\n" );
document.write( "(293-p)/(-2.5p+432.5) = 0.70<BR>\n" );
document.write( "293-p = 0.70(-2.5p+432.5)<BR>\n" );
document.write( "293-p = 0.70(-2.5p)+0.70(432.5)<BR>\n" );
document.write( "293-p = -1.75p+302.75<BR>\n" );
document.write( "-p+1.75p = 302.75-293<BR>\n" );
document.write( "0.75p = 9.75<BR>\n" );
document.write( "p = 9.75/0.75<BR>\n" );
document.write( "<font color=red>p = 13</font><BR>\n" );
document.write( "Rob moved <font color=red>13 pears</font> from crate B to crate A.\r<BR>\n" );
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document.write( "Use this value of p to find m.<BR>\n" );
document.write( "m = 1.5p + 134.5<BR>\n" );
document.write( "m = 1.5*13 + 134.5<BR>\n" );
document.write( "m = 19.5 + 134.5<BR>\n" );
document.write( "<font color=red>m = 154</font><BR>\n" );
document.write( "He also moved <font color=red>154 mangoes</font> from crate B to crate A.\r<BR>\n" );
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document.write( "Let's check the answers.<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD  colspan=2>Crate A</TD><TD  colspan=2>Crate B</TD></tr><tr><TD ></TD><TD ># of pears</TD><TD ># of mangoes</TD><TD ># of pears</TD><TD ># of mangoes</TD></tr><tr><TD >Before moving</TD><TD >207</TD><TD >176</TD><TD >293</TD><TD >274</TD></tr><tr><TD >After moving</TD><TD >207+13 = 220</TD><TD >176+154 = 330</TD><TD >293-13 = 280</TD><TD >274-154 = 120</TD></tr>\n" );
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document.write( "which cleans up a bit to this<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD  colspan=2>Crate A</TD><TD  colspan=2>Crate B</TD></tr><tr><TD ></TD><TD ># of pears</TD><TD ># of mangoes</TD><TD ># of pears</TD><TD ># of mangoes</TD></tr><tr><TD >Before moving</TD><TD >207</TD><TD >176</TD><TD >293</TD><TD >274</TD></tr><tr><TD >After moving</TD><TD >220</TD><TD >330</TD><TD >280</TD><TD >120</TD></tr>\n" );
document.write( "</TABLE>The table format is optional, but I find it helps to keep all the numbers organized. \r<BR>\n" );
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document.write( "After moving 13 pears and 154 mangoes from B to A, there are:<BR>\n" );
document.write( "220 pears out of 220+330 = 550 fruit in crate A.<BR>\n" );
document.write( "Then note how 220/550 = 0.40 = 40% to show that 40% of the fruit in crate A are pears.\r<BR>\n" );
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document.write( "So far so good.\r<BR>\n" );
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document.write( "After moving 13 pears and 154 mangoes from B to A, there are:<BR>\n" );
document.write( "280 pears left out of 280+120 = 400 fruit left in crate B.<BR>\n" );
document.write( "280/400 = 0.70 = 70%<BR>\n" );
document.write( "Showing that 70% of the fruit left in crate B are pears.\r<BR>\n" );
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document.write( "The answers are fully confirmed.\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "He moved <font color=red>13 pears</font> and <font color=red>154 mangoes</font> from crate B to crate A.<BR>\n" );
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