Question 344176
In words:
(amount of salt in final solution)/(total gallons of final solution)
=45%
Let {{{a}}} = gallons of 40% solution
Let {{{b}}} = gallons of 60% solution
given:
Amount of salt in 40% solution = {{{.4a}}}
Amount of salt in 60% solution = {{{.6b}}}
(1) {{{a + b = 100}}}
(2) {{{(.4a + .6b)/ 100 = .45}}}
(2) {{{.4a + .6b = 45}}} 
(2) {{{4a + 6b = 450}}}
Multiply both sides of (1) by {{{4}}} and
subtract (1) from (2)
(2) {{{4a + 6b = 450}}}
(1) {{{-4a - 4b = -400}}}
{{{2b = 50}}}
{{{b = 25}}} gallons
And, from (1)
{{{a + b = 100}}}
{{{a + 25 = 100}}}
{{{a = 75}}}
75 gallons of 40% solution and 25 gallons of 60% solution must be used
check answer:
{{{(.4a + .6b)/ 100 = .45}}}
{{{(.4*75 + .6*25)/100 - .45}}}
{{{(30 + 15)/100 = .45}}}
{{{45/100 = .45}}}
{{{.45 = .45}}}
OK