document.write( "Question 480615: Suppose z varies directly as x and y and inversely as w, and z =8 when x =6, y =5 and w =10. Find z when x =3, y =4 and w = 5. \n" ); document.write( "
Algebra.Com's Answer #329155 by Edwin McCravy(20056)\"\" \"About 
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Suppose z varies directly as x and y and inversely as w, and z =8 when x =6, y =5 and w =10. Find z when x =3, y =4 and w = 5.
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document.write( "FORMULA:\r\n" );
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document.write( "                          product of \"directly\" or \"jointly\" variables\r\n" );
document.write( "\"Varies as\" variable = k* --------------------------------------------\r\n" );
document.write( "                              product of \"inversely\" variables\r\n" );
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document.write( "The \"varies as\" variable is z, so write:\r\n" );
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document.write( "                   z = k*-----\r\n" );
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document.write( "The \"directly variables\" are x and y, so write them on the top:\r\n" );
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document.write( "                          xy\r\n" );
document.write( "                   z = k*----- \r\n" );
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document.write( "There is just one \"inversely variable\", w, so write it on the bottom:\r\n" );
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document.write( "                          xy\r\n" );
document.write( "                   z = k*----- \r\n" );
document.write( "                           w\r\n" );
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document.write( "Now we're ready to substitute the numbers for all the letters except the\r\n" );
document.write( "constant k from this: \"z =8 when x =6, y =5 and w =10\". Substituting:\r\n" );
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document.write( "                          6*5\r\n" );
document.write( "                   8 = k*----- \r\n" );
document.write( "                           10\r\n" );
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document.write( "Solve for k:\r\n" );
document.write( "                          30\r\n" );
document.write( "                   8 = k*-----\r\n" );
document.write( "                          10\r\n" );
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document.write( "                   8 = k*3\r\n" );
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document.write( "                  8\r\n" );
document.write( "                 --- = k\r\n" );
document.write( "                  3\r\n" );
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document.write( "Now go back to this equation:\r\n" );
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document.write( "                          xy\r\n" );
document.write( "                   z = k*----- \r\n" );
document.write( "                           w\r\n" );
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document.write( "and substitute 3/8 for the constant k.\r\n" );
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document.write( "                        3   xy\r\n" );
document.write( "                   z = ---*---- \r\n" );
document.write( "                        8    w\r\n" );
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document.write( "or\r\n" );
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document.write( "                        3xy\r\n" );
document.write( "                   z = ----- \r\n" );
document.write( "                         8w\r\n" );
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document.write( "Now we substitute in x =3, y =4 and w = 5, to find z:\r\n" );
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document.write( "                        3(3)(4)\r\n" );
document.write( "                   z = -------- \r\n" );
document.write( "                         8(5)\r\n" );
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document.write( "Then finish it up:\r\n" );
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document.write( "                        36\r\n" );
document.write( "                   z = ---- \r\n" );
document.write( "                        40\r\n" );
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document.write( "Reduce the fraction:\r\n" );
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document.write( "                   \r\n" );
document.write( "                         9\r\n" );
document.write( "                   z = ---- \r\n" );
document.write( "                        10\r\n" );
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document.write( "The answer is 9/10.\r\n" );
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document.write( "[In many problems one of the types of variables \"directly\", \"jointly\",\r\n" );
document.write( "or \"inversely\" variables are missing, in which case you put 1 for them.]\r\n" );
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document.write( "Edwin
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