Question 184451
Let {{{a}}} = ml of 25% solution needed
Let {{{b}}} = ml of 75% solution needed 
In words:
((salt in 25% solution) + (salt in 75% solution)) / (total amount of solution) =
 40%
given:
salt in 25% solution = {{{.25a}}} ml
salt in 75% solution = {{{.75b}}} ml
Total amount of solution = {{{50}}} ml
-------------------------
(1) {{{a + b = 50}}}
(2) {{{(.25a + .75b) / 50 = .40}}}
(2) {{{.25a + .75b = 20}}}
Multiply both sides of (1) by {{{.25}}}
(1) {{{.25a + .25b = 12.5}}}
Subtract (1) from (2)
(2) {{{.25a + .75b = 20}}}
(1) {{{-.25a - .25b = -12.5}}}
(3) {{{.50b = 7.5}}}
(3) {{{b = 15}}}
and
(1) {{{a + b = 50}}}
(1) {{{a + 15 = 50}}}
{{{a = 35}}}
35 ml of 25% solution and 15 ml of 75% solution are needed
check:
(2) {{{(.25a + .75b) / 50 = .40}}}
(2) {{{(.25*35 + .75*15) / 50 = .40}}}
(2) {{{(8.75 + 11.25) / 50 = .40}}}
(2) {{{ 20 / 50 = .40}}}
(2) {{{.40 = .40}}}
OK