document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138522>Question 1138522</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ben was describing his coin collection to his friends. He said I have 1.45 pesos more in 5 centavos (nickels) than in 10 centavos (dimes). Ii I had two 5 centavos (nickels) less, I would have 5 times as many 5 centavo (nickels) as 10 centavos (dimes). How many coins of each kind does he have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756391 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=756391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the number of persos needs to be 145 and not 1.45.\r<BR>\n" );
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document.write( "there are 100 pesos to the dollar.\r<BR>\n" );
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document.write( "therefore 1.45 dollars worth of pesos is equal to 145 pesos.\r<BR>\n" );
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document.write( "you could work this problem in dollars, but it's easier to work it in pesos.\r<BR>\n" );
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document.write( "i'll do both to sh ow you the difference.\r<BR>\n" );
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document.write( "you are given that the number of nickels is equal to the number of dimes plus 145 pesos.\r<BR>\n" );
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document.write( "the value of a nickel is 5 peros.\r<BR>\n" );
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document.write( "the value of a dime is 10 pesos.\r<BR>\n" );
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document.write( "if you let x equal the number of nickels and y equal the number of dimes, then your first equation is:\r<BR>\n" );
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document.write( "5x = 10y + 145.\r<BR>\n" );
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document.write( "this equations tells you that the number of nickels times 5 pesos per nickel is equal to the the number of dimes times 10 pesos per dime plus 145 pesos.\r<BR>\n" );
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document.write( "you are told that if you had 2 less nickels, then the number of nickels would be equal to 5 times the number of dimes.\r<BR>\n" );
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document.write( "the equation for this is x - 2 = 5y.\r<BR>\n" );
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document.write( "solve for x in this equation to get x = 5y + 2.\r<BR>\n" );
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document.write( "in the first equation of 5x = 10y + 145, replace x with 5y + 2 to get:\r<BR>\n" );
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document.write( "5 * (5y + 2) = 10y + 145\r<BR>\n" );
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document.write( "simplify to get 25y + 10 = 10y + 145\r<BR>\n" );
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document.write( "subtract 10y from both sides of the equation and subtract 10 from both sides of the equation to get:\r<BR>\n" );
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document.write( "25y - 10y = 145 - 10\r<BR>\n" );
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document.write( "simplify to get 15y = 135\r<BR>\n" );
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document.write( "solve for y to get y = 9.\r<BR>\n" );
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document.write( "since x is equal to 5y + 2, you get x = 47.\r<BR>\n" );
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document.write( "you have x = 47 and y = 9.\r<BR>\n" );
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document.write( "your original equation is 5x = 10y + 145.\r<BR>\n" );
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document.write( "replace x with 47 and y with 9 to get 5 * 47 =  10 * 9 = 145.\r<BR>\n" );
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document.write( "simplify to get 235 = 90 + 145 which becomes 235 = 235 which confirms the solution is correct.\r<BR>\n" );
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document.write( "now back to the beginning.\r<BR>\n" );
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document.write( "you were given 1.45 in pesos (not 1.45 pesos).\r<BR>\n" );
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document.write( "since you are working in dollars, then anickel is equal to .05 dollars and a dime is equal to .10 dollars.\r<BR>\n" );
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document.write( "your first equaiton becomes .05 * x = .10 * y + 1.45\r<BR>\n" );
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document.write( "you are then given that x - 2 = 5 * y which results in x = 5y + 2.\r<BR>\n" );
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document.write( "you then replace x with 5y + 2 to get .05 * (5y + 2) = .10 * y + 1.45\r<BR>\n" );
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document.write( "simplify to get .25 * y + .10 = .10 * y + 1.45\r<BR>\n" );
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document.write( "subtract .10 * y from both sides of the equation and subtract .10 from both sides of the equation to get:\r<BR>\n" );
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document.write( ".25 * y - .10 * y = 1.45 - .10\r<BR>\n" );
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document.write( "simplify to get .15 * y = 1.35\r<BR>\n" );
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document.write( "solve for y to get y = 9\r<BR>\n" );
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document.write( "since x = 5y + 2, you get x = 47.\r<BR>\n" );
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document.write( "replacing y with 9 and x with 47 in the original equation of .05 * x = .10 * y + 1.45 gets you.\r<BR>\n" );
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document.write( ".05 * 47 = .10 * 9 + 1.45 which results in 2.35 = .9 + 1.45 which results in 2.35 = 2.35 which confirms the solution is good.\r<BR>\n" );
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document.write( "the difference is that, the first time i worked in pesos and the second time i worked in dollars.\r<BR>\n" );
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document.write( "145 pesos equals 1.45 in dollars.\r<BR>\n" );
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document.write( "5 pesos per nickel equals .05 dollars per nickel.\r<BR>\n" );
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document.write( "10 pesos per dime equals .10 dollars per dime.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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