Question 718014
Let {{{ a }}} = kg of Kenyan coffee needed
Let {{{ b }}} = kg of Venezuelan coffee needed
given:
(1) {{{ a + b =  312 }}}
(2) {{{ ( 12a + 16b ) / 312 = 13 }}}
----------------------------
(2) {{{ 12a + 16b = 13*312 }}}
(2) {{{ 12a + 16b = 4056 }}}
Divide through by {{{ 4 }}}
(2) {{{ 3a + 4b = 1014 }}}
Multiply both sides of (1) by {{{ 3 }}} and
subtract (1) from (2)
(2) {{{ 3a + 4b = 1014 }}}
(1) {{{ -3a - 3b =  936 }}}
{{{ b = 78 }}}
and, since
(1) {{{ a + b =  312 }}}
(1) {{{ a = 234 }}}
234 kg of Kenyan coffee are needed
78 kg of Venezuelan coffee are needed
check:
(2) {{{ ( 12*234 + 16*78 ) / 312 = 13 }}}
(2) {{{  2808 + 1248 = 13*312 }}}
(2) {{{ 4056 =  4056 }}}
OK