Question 621229
Let {{{ a }}} = number of cups of 6% tea needed
Let {{{ b }}} = number of cups of 3% tea needed
{{{ .06a }}} = cups of sugar in 6% tea
{{{ .03b }}} = cups of sugar in 3% tea
-----------
(1) {{{ a + b = 9 }}}
(2) {{{ ( .06a + .03b ) / 9 = .04 }}}
-------------------------
(2) {{{ .06a + .03b = .36 }}}
(2) {{{ 6a + 3b = 36 }}}
(2) {{{ 2a + b = 12 }}}
Subtract (1) from (2)
(2) {{{ 2a + b = 12 }}}
(1) {{{ -a - b = -9 }}}
{{{ a = 3 }}}
and, since
(1) {{{ a + b = 9 }}}
(1) {{{ 3 + b = 9 }}}
(1) {{{ b = 6 }}}
3 cups of 6% tea are needed
6 cups of 3% tea are needed
check:
(2) {{{ ( .06a + .03b ) / 9 = .04 }}}
(2) {{{ ( .06*3 + .03*6 ) / 9 = .04 }}}
(2) {{{ ( .18 + .18 ) / 9 = .04 }}}
(2) {{{ .36/9 = .04 }}}
(2) {{{ .36 = .04*9 }}}
(2) {{{ .36 = .36 }}}
OK