Question 585605
Let {{{ a }}} = liters of 75% pesticide needed
Let {{{ b }}} = liters of 35% pesticide needed
given:
(1) {{{ a + b = 440 }}}
(2) {{{ ( .75a + .35b ) / 440 = .43 }}}
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(2) {{{ .75a + .35b = .43*440 }}}
(2) {{{ .75a + .35b = 189.2 }}}
(2) {{{ 75a + 35b = 18920 }}}
(2) {{{ 15a + 7b = 3784 }}}
Multiply both sides of (1) by {{{ 7 }}}
and subtract (1) from (2)
(2) {{{ 15a + 7b = 3784 }}}
(1) {{{ -7a - 7b = -3080 }}}
{{{ 8a = 704 }}}
{{{ a = 88 }}}
and, since
(1) {{{ a + b = 440 }}}
(1) {{{ 88 + b = 440 }}}
(1) {{{ b = 440 - 88 }}}
(1) {{{ b = 352 }}}
88 liters of 75% pesticide are needed
352 liters of 35% pesticide are needed
check:
(2) {{{ ( .75*88 + .35*352 ) / 440 = .43 }}}
(2) {{{ ( 66 + 123.2 ) / 440 = .43 }}}
(2) {{{ 189.2 / 440 = .43 }}}
(2) {{{ 189.2 = .43*440 }}}
(2) {{{ 189.2 = 189.2 }}}
OK