Question 658959
Let {{{a}}} = quarts of 40% solution needed
Let {{{b}}} = quarts of 60% solution needed
given:
(1) {{{ a + b = 90 }}}
(2) {{{ ( .4a + .6b ) / 90 = .5 }}}
--------------------------
(2) {{{ .4a + .6b = .5*90 }}}
(2) {{{ .4a + .6b = 45 }}}
(2) {{{ 4a + 6b = 450 }}}
--------------------
Multiply both sides of (1) by {{{ 4 }}}
and subtract (1) from (2)
(2) {{{ 4a + 6b = 450 }}}
(1) {{{ -4a - 4b = -360 }}}
{{{ 2b = 90 }}}
{{{ b = 45 }}}
and, since
(1) {{{ a + b = 90 }}}
(1) {{{ a + 45 = 90 }}}
(1) {{{ a = 45 }}}
45 quarts of 40% solution are needed
45 quarts of 60% solution are needed
check:
(2) {{{ ( .4*45 + .6*45 ) / 90 = .5 }}}
(2) {{{ ( 18 + 27 ) / 90 = .5 }}}
(2) {{{ 45 / 90 = .5 }}}
(2) {{{ 45 = .5*90 }}}
(2) {{{ 45 = 45 }}}
OK