Question 732067
Let {{{ a }}} = quarts of 25% solution needed
Let {{{ b }}} = quarts of pure antifreeze needed
given:
(1) {{{ a + b = 12 }}}
(2) {{{ ( .25a + b ) / 12 = .5 }}}
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(2) {{{ .25a + b = .5*12 }}}
(2) {{{ .25a + b = 6 }}}
(2) {{{ 25a + 100b = 600 }}}
(2) {{{ a + 4b = 24 }}}
Subtract (1) from (2)
(2) {{{ a + 4b = 24 }}}
(1) {{{ -a - b = -12 }}}
{{{ 3b = 12 }}}
{{{ b = 4 }}}
and, since
(1) {{{ a + b = 12 }}}
(1) {{{ a = 8 }}}
8 quarts of 25% solution are needed
4 quarts of pure antifreeze are needed
check:
(2) {{{ ( .25*8 + 4 ) / 12 = .5 }}}
(2) {{{ ( 2 + 4 ) / 12 = .5 }}}
(2) {{{ 6/12 = .5 }}}
(2) {{{ 6 = 6 }}}
OK