Question 638941
Let {{{ a }}} = pounds of 50 cents/pound candy needed
Let {{{ b }}} = pounds of 90 cents/pound candy needed
given:
(1) {{{ a + b = 75 }}}
(2) {{{ ( .5a + .9b ) / 75 = .76  }}}
------------------------
(2) {{{ .5a + .9b = 75*.76 }}}
(2) {{{ .5a + .9b = 57 }}}
(2) {{{ 5a + 9b = 570 }}}
Multiply both sides of (1) by {{{ 5 }}}
and subtract (1) from (2)
(2) {{{ 5a + 9b = 570 }}}
(1) {{{ -5a - 5b = -375 }}}
{{{ 4b = 195 }}}
{{{ b = 48.75 }}}
and, since
(1) {{{ a + b = 75 }}}
(1) {{{ a + 48.75 = 75 }}}
(1) {{{ a = 26.25 }}}
26.25 pounds of 50 cents/pound candy are needed
48.75 pounds of 90 cents/pound candy are needed
check:
(2) {{{ ( .5a + .9b ) / 75 = .76  }}}
(2) {{{ ( .5*26.25 + .9*48.75 ) / 75 = .76  }}}
(2) {{{ ( 13.125 + 43.875 ) / 75 = .76  }}}
(2) {{{ 57/75 = .76 }}}
(2) {{{ 57 = .76*75 }}}
(2) {{{ 57 = 57 }}}
OK