document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170974>Question 1170974</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three friends A, B and C dine out and decide to split the bill according to what they order. A's portion and B's protion of the bil totalled $35, while B's portion was $5 less than C's portion of the bill. The ratio of A's portion to C's portion of the bill is 4:5. Determine the total bill amount? </SPAN>\n" );
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document.write( "A = friend A's portion<BR>\n" );
document.write( "B = friend B's portion<BR>\n" );
document.write( "C = friend C's portion<BR>\n" );
document.write( "A,B,C are positive real numbers and are values in dollars.\r<BR>\n" );
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document.write( "\"A's portion and B's protion of the bil totalled $35\"<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "A+B = 35\r<BR>\n" );
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document.write( "\"B's portion was $5 less than C's portion\" <BR>\n" );
document.write( "means that<BR>\n" );
document.write( "B = C - 5\r<BR>\n" );
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document.write( "Go back to the first equation. Plug in B = C-5. Isolate C.<BR>\n" );
document.write( "A+B = 35<BR>\n" );
document.write( "A+C-5 = 35<BR>\n" );
document.write( "A+C = 35+5<BR>\n" );
document.write( "A+C = 40<BR>\n" );
document.write( "C = 40-A\r<BR>\n" );
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document.write( "The ratio of A to C is 4:5, which means,<BR>\n" );
document.write( "A/C = 4/5<BR>\n" );
document.write( "5A = 4C .... cross multiply<BR>\n" );
document.write( "5A = 4(40-A) .... plug in C = 40-A<BR>\n" );
document.write( "5A = 160-4A<BR>\n" );
document.write( "5A+4A = 160<BR>\n" );
document.write( "9A = 160<BR>\n" );
document.write( "A = 160/9<BR>\n" );
document.write( "A = 17.7777777777778 ....  which is approximate<BR>\n" );
document.write( "A = 17.78 ....  rounding to two decimal places\r<BR>\n" );
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document.write( "With this value of A, we can then find:<BR>\n" );
document.write( "C = 40-A<BR>\n" );
document.write( "C = 40-17.78<BR>\n" );
document.write( "C = 22.22\r<BR>\n" );
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document.write( "And,<BR>\n" );
document.write( "B = C - 5<BR>\n" );
document.write( "B = 22.22 - 5<BR>\n" );
document.write( "B = 17.22\r<BR>\n" );
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document.write( "In summary, we found:<BR>\n" );
document.write( "A's portion = $17.78<BR>\n" );
document.write( "B's portion = $17.22<BR>\n" );
document.write( "C's portion = $22.22\r<BR>\n" );
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document.write( "This means,<BR>\n" );
document.write( "Total Bill = A+B+C = 17.78+17.22+22.22 = 57.22 dollars\r<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "Total Bill = $57.22<BR>\n" );
document.write( "</font> </SPAN>\n" );
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