document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201145>Question 1201145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Adam’s annual salary is RM120,000 and his total expenses is RM90,000. His salary increases<BR>\n" );
document.write( "by RM12,000 each year while his expenses increase by RM15,000 each year. Each year, he<BR>\n" );
document.write( "saves the excess of his income.<BR>\n" );
document.write( "a) Represent his total savings as series.<BR>\n" );
document.write( "b) If Adam continues to manage his finances this way, after how many years will he has<BR>\n" );
document.write( "nothing left to save?<BR>\n" );
document.write( "c) Adam calculates that if his expenses increase by 𝑥 RM every year (instead of RM15,000<BR>\n" );
document.write( "each year), he will spend as much as he earns in the 25th<BR>\n" );
document.write( "year. Determine 𝑥.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835403 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835403\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Adam’s annual salary is RM120,000 and his total expenses is RM90,000. \r<BR>\n" );
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document.write( "His salary increases by RM12,000 each year while his expenses increase by RM15,000 each year.<BR>\n" );
document.write( "Represent his total savings as series.\r<BR>\n" );
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document.write( " (120000-90000)+(144000-105000)+(156000-120000)....<BR>\n" );
document.write( "(120000+144000+156000)... -(90000+105000+120000)...<BR>\n" );
document.write( "Let n be the number of years when income = expenses<BR>\n" );
document.write( "Both are arthimatic sequences<BR>\n" );
document.write( "Tn= a+(n-1)d<BR>\n" );
document.write( "a=120000<BR>\n" );
document.write( "d =12000<BR>\n" );
document.write( "tn= 120000 +(n-1)12000<BR>\n" );
document.write( "=  108000 +12000n\r<BR>\n" );
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document.write( "Expense after n years<BR>\n" );
document.write( "Tn= 90000+(n-1)15000<BR>\n" );
document.write( "= 75000+15000n\r<BR>\n" );
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document.write( "Income = expense\r<BR>\n" );
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document.write( "108000 +12000n=75000+15000n\r<BR>\n" );
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document.write( "3000n =33000<BR>\n" );
document.write( "n=11    Eleventh year there is no saving\r<BR>\n" );
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document.write( "Let x be the expence increase every year<BR>\n" );
document.write( "number of years = 25 when saving is nil<BR>\n" );
document.write( "T25= 120000 +(25-1)12000<BR>\n" );
document.write( "= 120000 +288000<BR>\n" );
document.write( "= 408000\r<BR>\n" );
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document.write( "408000 = 90000 +(25-1)x<BR>\n" );
document.write( "408000  -  90000=24x\r<BR>\n" );
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document.write( "318000=24x\r<BR>\n" );
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document.write( "x= 13250 expence increase every year\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );