Question 885821
Let {{{ a }}} = liters of the 64% fertilizer needed
Let {{{ b }}} = liters of the 22% fertilizer needed
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(1) {{{ a + b = 84 }}}
(2) {{{ (( .64a + .22b )) / 84 = .57 }}}
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(2) {{{ .64a + .22b = .57*84 }}}
(2) {{{ .64a + .22b = 47.88 }}}
(2) {{{ 64a + 22b = 4788 }}}
(2) {{{ 32a + 11b = 2394 }}}
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Multiply both sides of (1) by {{{ 32 }}}
and subtract (2) from (1)
(1) {{{ 32a + 32b = 2688 }}}
(2) {{{ -32a - 11b = -2394 }}}
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{{{ 21b = 294 }}}
{{{ b = 14 }}}
and, since
(1) {{{ a + b = 84 }}}
(1) {{{ a = 84 - 14 }}}
(1) {{{ a = 70 }}}
70 liters of the 64% solution are needed
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check:
(2) {{{ ( .64a + .22b ) / 84 = .57 }}}
(2) {{{ ( .64*70 + .22*14 ) / 84 = .57 }}}
(2) {{{ ( 44.8 + 3.08 ) / 84 = .57 }}}
(2) {{{ 47.88 = .57*84 }}}
(2) {{{ 47.88 = 47.88 }}}
OK