Question 629214
Let {{{ a }}} = grams of 40% ointment needed
Let {{{ b }}} = grams of 10% ointment needed
given:
(1) {{{ a + b = 90 }}}
(2) {{{ ( .4a + .1b ) / 90 = .2 }}}
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(2) {{{ .4a + .1b = .2*90 }}}
(2) {{{ .4a + .1b = 18 }}}
(2) {{{ 4a + b = 180 }}}
Subtract (1) from (2) 
(2) {{{ 4a + b = 180 }}}
(1) {{{ -a - b = -90 }}}
{{{ 3a = 90 }}}
{{{ a = 30 }}}
and, since
(1) {{{ a + b = 90 }}}
(1) {{{ 30 + b = 90 }}}
(1) {{{ b = 60 }}}
30 grams of 40% ointment are needed
60 grams of 10% ointment are needed
check:
(2) {{{ ( .4*30 + .1*60 ) / 90 = .2 }}}
(2) {{{ ( 12 + 6 ) / 90 = .2 }}}
(2) {{{ 18/90 = .2 }}}
(2) {{{ 18 = 18 }}}
OK