Question 696763
Let {{{ a }}} = ounces of 1% solution needed
Let {{{ b }}} = ounces of 50% solution needed
given:
(1) {{{ a+ b = 8 }}}
(2) {{{ ( .01a + .5b ) / 8 = .2 }}}
--------------------------
(2) {{{ .01a + .5b = .2*8 }}}
(2) {{{ .01a + .5b = 1.6 }}}
(2) {{{ a + 50b = 160 }}}
Subtract (1) from (2)
(2) {{{ a + 50b = 160 }}}
(1) {{{ -a- b = -8 }}}
{{{ 49b = 152 }}}
{{{ b = 3.102 }}}
and, since
(1) {{{ a+ b = 8 }}}
(1) {{{ a = 8 - b }}}
(1) {{{ a = 8 - 3.102 }}}
(1) {{{ a = 4.898 }}}
4.898 ounces of 1% solution are needed
3.102 ounces of 50% solution are needed
check:
(2) {{{ ( .01a + .5b ) / 8 = .2 }}}
(2) {{{ ( .01*4.898 + .5*3.102 ) / 8 = .2 }}}
(2) {{{ .04898 + 1.551 = .2*8 }}}
(2) {{{ 1.59998 = 1.6 }}}
close enough- error due to rounding off