document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187633>Question 1187633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.) A bank requires a monthly payment of 450.75 Php for a loan of 54,000 Php. At the same rate, what is the monthly payment for a loan of 90,000 Php?\r<BR>\n" );
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document.write( "2.)Thirty workers can finish a house in 25 days. by working at the same rate, how many days will it take 25 workers to finish the house? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818642 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 90/54 * 450.75 = 751.25.\r<BR>\n" );
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document.write( "all other things being equal, i think it will be a straight ratio to find the larger payment.\r<BR>\n" );
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document.write( "i checked with an online calculator to see if that was true.<BR>\n" );
document.write( "it was.\r<BR>\n" );
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document.write( "here's the results of my finding.\r<BR>\n" );
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document.write( "first i found the interest rate.\r<BR>\n" );
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document.write( "then i changed the present value to 90,000 from 54,000.\r<BR>\n" );
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document.write( "the monthly payment for the 90,000 dollar loan was 90/54 * 450.75 = 751.25, confirming the ratio formula worked as long as the number of payments remained the same and the interest rate remained the same.\r<BR>\n" );
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document.write( "it appears the monthly payment is directly proportional to the amount of the investment as long as all other factors remain the same.\r<BR>\n" );
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document.write( "with direct propportion, the formula is y = k * x<BR>\n" );
document.write( "when y = 54000 and x = 450.75, solve for k to get:<BR>\n" );
document.write( "k = 54000 / 450.75.\r<BR>\n" );
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document.write( "when y = 90000 and k = 54000 / 450.75, the formula becomes:<BR>\n" );
document.write( "90000 = 54000 / 450.75 * x<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 90000 / (54000 / 450.75) = 90000 * 450.75 / 54000 = 751.25.\r<BR>\n" );
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document.write( "thirty workers finish in 25 days.<BR>\n" );
document.write( "25 workers, working at the same rate, should finish in 25/30 * 25 = 20.833333..... days.<BR>\n" );
document.write( "i used the rate * people * time = quantity formula to see what the relationship would be.<BR>\n" );
document.write( "with 30 workers, the formula becomes rate * 30 * 25 = 1<BR>\n" );
document.write( "the rate is the rate that each person works at.<BR>\n" );
document.write( "people is the number of people involved.<BR>\n" );
document.write( "time is how long it takes.<BR>\n" );
document.write( "1 = the quantity, which is one finished house.<BR>\n" );
document.write( "solve for rate to get:<BR>\n" );
document.write( "rate = 1/(30*25) = 1/750.<BR>\n" );
document.write( "this says that each person can finish 1/750 of the house in 1 day.<BR>\n" );
document.write( "with 30 people, then all 30 can finish 1/25 of the house in 1 day.<BR>\n" );
document.write( "the whole house can then be finished in 25 days.\r<BR>\n" );
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document.write( "the rate of each person is 1/750 of the house in one day.<BR>\n" );
document.write( "this remains the same.<BR>\n" );
document.write( "the formula for 30 people becomes 1/750 * 30 * 25 = 1<BR>\n" );
document.write( "1/750 is the rate of each person.<BR>\n" );
document.write( "30 is the number of people.<BR>\n" );
document.write( "25 is the number of days.<BR>\n" );
document.write( "1 is the quantity of work performed.<BR>\n" );
document.write( "evaluate the equation to get 1 = 1, confirming the values are good.\r<BR>\n" );
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document.write( "when the rate of each person remains the same and the number of people becomes 25 instead of 30, the formula becomes:<BR>\n" );
document.write( "1/750 * 25 * number of days = 1<BR>\n" );
document.write( "solve for number of days to get:<BR>\n" );
document.write( "number of days = 1/(1/750 * 25) = 1/(25/750) = 1*750/25 = 30<BR>\n" );
document.write( "1/750 is the rate of each person.<BR>\n" );
document.write( "25 is the number of people.<BR>\n" );
document.write( "30 is the number of days.<BR>\n" );
document.write( "1 is the quantity of work performed.\r<BR>\n" );
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document.write( "it appears like the number of days is inversely proportional to the number of workers as long as all other factors remain the same.\r<BR>\n" );
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document.write( "the inverse proportion formula is y = k/x<BR>\n" );
document.write( "when y = number of days and x = number of workers, the formula becomes:<BR>\n" );
document.write( "25 = k/30<BR>\n" );
document.write( "solve for k to get:<BR>\n" );
document.write( "k = 750.<BR>\n" );
document.write( "when x = 25, the formula becomes:<BR>\n" );
document.write( "y = 750/25.<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = 30.\r<BR>\n" );
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document.write( "the relationship between the direct and inverse proportion formulas is not that easy to see, which is why i always go to the basic formulas of:<BR>\n" );
document.write( "rate * time = quantity.<BR>\n" );
document.write( "rate * number of people * time = quantity.<BR>\n" );
document.write( "when number of people are involved, i use the rate * number of people * time = quantity formula.<BR>\n" );
document.write( "when number of people are not involved, i use the rate * time = quantity formula.\r<BR>\n" );
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document.write( "if i really think about it, .....\r<BR>\n" );
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document.write( "assuming people are involved, the formula is:<BR>\n" );
document.write( "rate * number of people * time = quantity.<BR>\n" );
document.write( "assuming rate and quantity are always the same, then solve for number of people * time to get:<BR>\n" );
document.write( "number of people * time = quantity / rate.<BR>\n" );
document.write( "since quantity / rate is always the same, then set it equal to k.<BR>\n" );
document.write( "formula becomes:<BR>\n" );
document.write( "number of people * time = k<BR>\n" );
document.write( "solve for time to get time = k / number of people.<BR>\n" );
document.write( "solve for number of people to get number of people = k / time.<BR>\n" );
document.write( "both of these are inverse ratio type problems.\r<BR>\n" );
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document.write( "i never really connected it this way before, but it makes sense, and confirms that the relationship is an inverse relationship.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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