Question 640216
Let {{{ a }}} = quarts of 40% solution needed
Let {{{ b }}} = quarts of 10% solution needed
given:
(1) {{{ a + b = 300 }}}
(2) {{{ ( .4a + .1b ) / 300 = .3 }}}
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(2) {{{ .4a + .1b = .3*300 }}}
(2) {{{ .4a + .1b = 90 }}}
(2) {{{ 4a + b = 900 }}}
Subtract (1) from (2)
(2) {{{ 4a + b = 900 }}}
(1) {{{ -a - b = -300 }}}
{{{ 3a = 600 }}}
{{{ a = 200 }}}
and since
(1) {{{ a + b = 300 }}}
(1) {{{ b = 100 }}}
200 quarts of 40% solution is needed
100 quarts of 10% solution is needed
check:
(2) {{{ ( .4*200 + .1*100 ) / 300 = .3 }}}
(2) {{{ ( 80 + 10 ) / 300 = .3 }}}
(2) {{{ 90 / 300 = .3 }}}
(2) {{{ 90 = .3*300 }}}
(2) {{{ 90 = 90 }}}
OK