Question 1076102
Let {{{ a }}} = grams of 30% gold needed
Let {{{ b }}} = grams of 80% gold needed
-------------------------------------
(1) {{{ a + b = 50 }}}
(2) {{{ ( .3a + .8b ) / 50 = .68 }}}
-------------------------------------
(2) {{{ .3a + .8b = 34 }}}
(2) {{{ 3a + 8b = 340 }}}
------------------------------
Multiply both sides of (1) by {{{ 3 }}} and
subtract (1) from (2)
--------------------------------------
(2) {{{ 3a + 8b = 340 }}}
(1) {{{ -3a - 3b = -150 }}}
--------------------------
{{{ 5b = 190 }}}
{{{ b = 38 }}}
and
(1) {{{ a + 38 = 50 }}}
(1) {{{ a = 12 }}}
----------------------
12 grams of 30% gold are needed
38 grams of 80% gold are needed
--------------------------------
check:
(2) {{{ ( .3a + .8b ) / 50 = .68 }}}
(2) {{{ ( .3*12 + .8*38 ) / 50 = .68 }}}
(2) {{{ ( 3.6 + 30.4 ) / 50 = .68 }}}
(2) {{{ 34 = .68*50 }}}
(2) {{{ 34 = 34 }}}
OK