Question 725240
Let {{{ a }}} = pounds of 22% fertilizer needed
Let {{{ b }}} = pounds of 4% fertilizer needed
given:
(1) {{{ a + b = 400 }}}
(2) {{{ ( .22a + .04b ) / 400 = .1 }}}
-----------------------------
(2) {{{ .22a + .04b = .1*400 }}}
(2) {{{ 22a + 4b = 4000 }}}
(2) {{{ 11a + 2b = 2000 }}}
Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 11a + 2b = 2000 }}}
(1) {{{ -2a - 2b = -800 }}}
{{{ 9a = 1200 }}}
{{{ a = 133.33 }}}
and
(1) {{{ a + b = 400 }}}
{{{ b = 266.67 }}}
133.33 pounds of 22% fertilizer are needed
266.67 pounds of 4% fertilizer are needed 
check:
(2) {{{ ( .22a + .04b ) / 400 = .1 }}}
(2) {{{ ( .22*133.33 + .04*266.67 ) / 400 = .1 }}}
(2) {{{ ( 29.3326 + 10.6668 ) / 400 = .1 }}}
(2) {{{ 29.3326 + 10.6668 = 40 }}}
(2) {{{ 39.9994 = 40 }}}
close enough