document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201935>Question 1201935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For positive numbers a, b, and c, if 2ab = 1, 3bc = 2, and 4ca = 3, what is the value of a + b + c ?\r<BR>\n" );
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document.write( "(A) 29/12<BR>\n" );
document.write( "(B) 9/4<BR>\n" );
document.write( "(C) 25/12<BR>\n" );
document.write( "(D) 23/12<BR>\n" );
document.write( "(E) 7/4 </SPAN>\n" );
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document.write( "Answer: <font color=red size=4>Choice (A)  29/12</font>\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "I'll label the equations eq1, eq2, and eq3\r<BR>\n" );
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document.write( "Divide eq1 over eq2.<BR>\n" );
document.write( "The LHS (left hand sides) and RHS (right hand sides) will divide separately.\r<BR>\n" );
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document.write( "eq1/eq2 <BR>\n" );
document.write( "(2ab)/(3bc) = 1/2<BR>\n" );
document.write( "(2a)/(3c) = 1/2<BR>\n" );
document.write( "a/c = (1/2)*(3/2)<BR>\n" );
document.write( "a/c = 3/4<BR>\n" );
document.write( "4a = 3c\r<BR>\n" );
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document.write( "Now multiply both sides by 'c' so the 4a becomes 4ca.\r<BR>\n" );
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document.write( "c*4a = c*3c<BR>\n" );
document.write( "4ca = 3c^2 <BR>\n" );
document.write( "3 = 3c^2 ... replace 4ca with 3; valid because of eq3<BR>\n" );
document.write( "3c^2 = 3 <BR>\n" );
document.write( "c^2 = 3/3<BR>\n" );
document.write( "c^2 = 1<BR>\n" );
document.write( "c = sqrt(1) ... since c is positive<BR>\n" );
document.write( "c = 1\r<BR>\n" );
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document.write( "Go back to eq3 to determine 'a'.<BR>\n" );
document.write( "4ca = 3<BR>\n" );
document.write( "4*1a = 3<BR>\n" );
document.write( "4a = 3<BR>\n" );
document.write( "a = 3/4\r<BR>\n" );
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document.write( "Now use either eq1 or eq2 to find b<BR>\n" );
document.write( "2ab = 1<BR>\n" );
document.write( "2*(3/4)*b = 1<BR>\n" );
document.write( "(6/4)*b = 1<BR>\n" );
document.write( "(3/2)*b = 1<BR>\n" );
document.write( "b = 1*(2/3)<BR>\n" );
document.write( "b = 2/3<BR>\n" );
document.write( "or<BR>\n" );
document.write( "3bc = 2<BR>\n" );
document.write( "3b*1 = 2<BR>\n" );
document.write( "3b = 2<BR>\n" );
document.write( "b = 2/3\r<BR>\n" );
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document.write( "We found these values<BR>\n" );
document.write( "a = 3/4<BR>\n" );
document.write( "b = 2/3<BR>\n" );
document.write( "c = 1\r<BR>\n" );
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document.write( "Add them up.<BR>\n" );
document.write( "a + b + c<BR>\n" );
document.write( "(3/4) + (2/3) + 1<BR>\n" );
document.write( "(3/4)*(3/3) + (2/3)*(4/4) + 1*(12/12)<BR>\n" );
document.write( "(9/12) + (8/12) + (12/12)<BR>\n" );
document.write( "(9+8+12)/12<BR>\n" );
document.write( "<font color=red>29/12</font>\r<BR>\n" );
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document.write( "Extra info:<BR>\n" );
document.write( "The improper fraction 29/12 converts to the mixed number 2 & 5/12 because of the scratch work below.<BR>\n" );
document.write( "29/12 = (24+5)/12<BR>\n" );
document.write( "29/12 = (24/12)+(5/12)<BR>\n" );
document.write( "29/12 = 2+(5/12)<BR>\n" );
document.write( "29/12 = 2 & 5/12<BR>\n" );
document.write( "Or you could use long division to find that 29/12 = 2 remainder 5. Both of these values are found in \"2 & 5/12\".<BR>\n" );
document.write( "The template is quotient & remainder/12.\r<BR>\n" );
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document.write( "29/12 = 2.41667 approximately<BR>\n" );
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