Question 51387
{{{ 69.72 = 68.9257x + 70.9249(1-x) }}} expands to {{{ 69.72 = 68.9257x + 70.9249*1 - 70.9249*x) }}}, or {{{ 69.72 = 68.9257x + 70.9249 - 70.9249x }}}.  Adding like terms on the right side of the equation produces {{{ 69.72 = 70.9249 - 1.9992x }}}.  Now subtract 70.9249 from both sides.  This produces the equation {{{ 69.72 - 70.9249 = 70.9249 - 1.9992x - 70.9249 }}} which reduces to {{{ -1.2049 = -1.9992x }}}.  Dividing both sides by -1.9992 yields equation {{{ -1.2049 / -1.9992 = -1.9992x / -1.9992 }}}, which reduces to {{{ .602691 = x }}}.  To check our answer, substitute it into the original equation for x, producing {{{ 69.72 = 68.9257*.602691 + 70.9249*(1-.602691) }}}.  Simplifying this equation produces {{{ 69.72 = 41.555993 + 70.9249*.39709 }}}.  Simplifiying further yields {{{ 69.72 = 41.55599 + 28.163568 }}}, which produces {{{ 69.72 = 69.719561 }}}.  Rounding to the nearest hundredth produces 69.72 = 69.72, a true statement, which means our answer of {{{ x = .602691 }}} is correct.