Question 954363
Let {{{ a }}} = ml of 45% solution needed
{{{ .45a }}} = ml of phosphorus in 45% solution
Let {{{ b }}} = ml of 18% solution needed
{{{ .18b }}} = ml of phosphorus in 18% solution
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(1) {{{ a + b = 12 }}}
(2) {{{ ( .45a + .18b ) / 12 = .36 }}}
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(2) {{{ .45a + .18b = .36*12 }}}
(2) {{{ .45a + .18b = 4.32 }}}
(2) {{{ 45a + 18b = 432 }}}
Divide both sides by {{{ 9 }}}
(2) {{{ 5a + 2b = 48 }}}
Multiply both sides of (1) by {{{2}}} and
subtract (1) from (2)
(2) {{{ 5a + 2b = 48 }}}
(1) {{{ -2a - 2b = -24 }}}
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{{{ 3a = 24 }}}
{{{ a = 8 }}}
and
(1) {{{ 8 + b = 12 }}}
(1) {{{ b = 4 }}}
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4 ml of the 18% solution are needed
check:
(2) {{{ ( .45a + .18b ) / 12 = .36 }}}
(2) {{{ ( .45*8 + .18*4 ) / 12 = .36 }}}
(2) {{{ ( 3.6 + .72 ) / 12 = .36 }}}
(2) {{{ 4.32 = .36*12 }}}
(2) {{{ 4.32 = 4.32 }}}
OK