Question 1046990
You need to end up with:
{{{ .245*100 = 24.5 }}} ml of alcohol
--------------------
Let the amounts in ml of the 3 solutions = 
{{{ a }}}, {{{ b }}}, and {{{ c }}}
given:
{{{ a = 2b }}}
--------------
(1) {{{ 2b + b + c = 100 }}} ml
(2) {{{ .1*( 2b ) + .15b + .3c = 24.5 }}}
------------------------------------
(1) {{{ 3b + c = 100 }}}
(2) {{{ .2b + .15b + .3c = 24.5 }}}
(2) {{{ .35b + .3c = 24.5 }}}
(2) {{{ 35b + 30c = 2450 }}}
-------------------------------
Multiply both sides of (1) by {{{ 30 }}} and
and subtract (2) from (1)
---------------------------
(1) {{{ 90b + 30c = 3000 }}}
(2) {{{ -35b - 30c = 2450 }}}
--------------------------
{{{ 55b = 550 }}}
{{{ b = 10 }}}
and
{{{ a = 2b }}}
{{{ a = 2*10 }}}
{{{ a = 20 }}}
and
(1) {{{ 3b + c = 100 }}}
(1) {{{ 3*10 + c = 100 }}}
(1) {{{ c = 70 }}}
------------------------
The chemist needs:
20 ml of A
10 ml of B
70 ml of C
--------------
check:
(2) {{{ 35b + 30c = 2450 }}}
(2) {{{ 35*10 + 30*70 = 2450 }}}
(2) {{{ 350 + 2100 = 2450 }}}
(2) {{{ 2450 = 2450 }}}
OK