Question 1014810
Let {{{ a }}} = pounds of $2.75/ lb coffee needed
Let {{{ b }}} = pounds of $5.00/ lb coffee needed
Assume total of 100 pounds of blend
----------------------------------
(1) {{{ a + b = 100 }}}
(2) {{{ ( 2.75a + 5b ) / 100 = 3.9 }}}
---------------------------------
(2) {{{ 2.75a + 5b = 390 }}}
(2) {{{ 275a + 500b = 39000 }}}
(2) {{{ 11a + 20b = 1560 }}}
Multiply both sides of (1) by {{{ 11 }}}
and subtract (1) from (2)
(2) {{{ 11a + 20b = 1560 }}}
(1) {{{ -11a - 11b = -1100 }}}
--------------------------
{{{ 9b = 460 }}}
{{{ b = 51.11 }}}
and
(1) {{{ a + b = 100 }}}
(1) {{{ a = 48.89 }}}
48.89 pounds of $2.75/ lb coffee are needed
51.11 pounds of $5.00/ lb coffee are needed
---------------------------------------
check:
(2) {{{ ( 2.75a + 5b ) / 100 = 3.9 }}}
(2) {{{ ( 2.75*48.89 + 5*51.11 ) / 100 = 3.9 }}}
(2) {{{ ( 134.45 + 255.55 ) / 100 = 3.9 }}}
(2) {{{ 390 = 390 }}}
OK