Question 996276
Let {{{ a }}} = ounces of the 3% solution needed
Let {{{ b }}} = ounces of the 5% solution needed
-----------------------
(1) {{{ a + b = 10 }}}
(2) {{{ ( .03a + .05b ) / 10 = .038 }}}
------------------------------
(2) {{{ .03a + .05b = .38 }}}
(2) {{{ 3a + 5b = 38 }}}
--------------------
Multiply both sides of (1) by {{{ 3 }}} and
subtract (1) from (2)
(2) {{{ 3a + 5b = 38 }}}
(1) {{{ -3a - 3b = -30 }}}
--------------------
{{{ 2b = 8 }}}
{{{ b = 4 }}}
and
(1) {{{ a + b = 10 }}}
(1) {{{ a + 4 = 10 }}}
(1) {{{ a = 6 }}}
6 ounces of the 3% solution are needed
---------------
check:
(2) {{{ ( .03a + .05b ) / 10 = .038 }}}
(2) {{{ ( .03*6 + .05*4 ) / 10 = .038 }}}
(2) {{{ ( .18 + .2 ) / 10 = .038 }}}
(2) {{{ .38 = 10*.038 }}}
(2) {{{ .38 = .38 }}}
OK