Question 660804
Let {{{ a }}} = liters of 40% solution needed
Let {{{ b }}} = liters of 25% solution needed
{{{ .4a }}} = liters of HN03 in 40% solution
{{{ .25b }}} = liters of HN03 in 25% solution
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(1) {{{ ( .4a + .25b ) / 57 = .26 }}}
(2) {{{ a + b = 57 }}}
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(1) {{{ .4a + .25b = .26*57 }}}
(1) {{{ .4a + .25b = 14.82 }}}
(1) {{{ 40a + 25b = 1482 }}}
Multiply both sides of (2) by {{{ 25 }}}
and subtract (2) from (1)
(1) {{{ 40a + 25b = 1482 }}}
(2) {{{ -25a - 25b = -1425 }}}
{{{ 15a = 57 }}}
{{{ a = 3.8 }}}
and, since
(2) {{{ a + b = 57 }}}
(2) {{{ 3.8 + b = 57 }}}
(2) {{{ b = 53.2 }}}
3.8 liters of 40% solution are needed
53.2 liters of 25% solution are needed
check:
(1) {{{ ( .4a + .25b ) / 57 = .26 }}}
(1) {{{ ( .4*3.8 + .25*53.2 ) / 57 = .26 }}}
(1) {{{ ( 1.52 + 13.3 ) / 57 = .26 }}}
(1) {{{ 14.82 = .26*57 }}}
(1) {{{ 14.82 = 14.82 }}}
OK