Question 749228
Let {{{ a }}} = liters of solution A needed
Let {{{ b }}} = liters of solution B needed
{{{ .12a }}} = liters of acid in solution A
{{{ .04b }}} = liters of acid in solution B
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(1) {{{ a + b = 60 }}}
(2) {{{ ( .12a + .04b ) / 60 = .1 }}}
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(2) {{{ .12a + .04b = 6 }}}
(2) {{{ 12a + 4b = 600 }}}
Multiply both sides of (1) by {{{ 4 }}} and
subtract (1) from (2)
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(2) {{{ 12a + 4b = 600 }}}
(1) {{{ -4a -4b = -240 }}}
{{{ 8a = 360 }}}
{{{ a = 45 }}}
and, since
(1) {{{ a + b = 60 }}}
(1) {{{ 45 + b = 60 }}}
(1) {{{ b = 15 }}}
45 liters of solution A are needed
15 liters of solution B are needed
check:
(2) {{{ ( .12a + .04b ) / 60 = .1 }}}
(2) {{{ ( .12*45 + .04*15 ) / 60 = .1 }}}
(2) {{{ ( 5.4 + .6 ) / 60 = .1 }}}
(2) {{{ 6 = .1*60 }}}
(2) {{{ 6 = 6 }}}
OK