Question 621351
Let {{{ a }}} = liters of 28% solution needed
Let {{{ b }}} = liters of 14% solution needed
{{{ .28a }}} = liters of sulfuric acid in 28% solution
{{{ .14b }}} = liters of sulfuric acid in 14% solution
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(1) {{{ a + b = 7 }}}
(2) {{{ ( .28a + .14b ) / 7 = .24 }}}
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(2) {{{ .28a + .14b = 1.68 }}}
(2) {{{ 28a + 14b = 168 }}}
(2) {{{ 2a + b = 12 }}}
Subtract (1) from (2)
(2) {{{ 2a + b = 12 }}}
(1) {{{ -a - b = -7 }}}
{{{ a = 5 }}}
and, since
(1) {{{ a + b = 7 }}}
(1) {{{ 5 + b = 7 }}}
(1) {{{ b = 2 }}}
5 liters of 28% solution are needed
2 liters of 14% solution are needed
check:
(2) {{{ ( .28a + .14b ) / 7 = .24 }}}
(2) {{{ ( .28*5 + .14*2 ) / 7 = .24 }}}
(2) {{{ ( 1.4 + .28 ) / 7 = .24 }}}
(2) {{{ 1.68/7 = .24 }}}
(2) {{{ 1.68 = 1.68 }}}
OK