Question 301657
Let {{{a}}} = ml of 8% solution needed
Let {{{b}}} = ml of 3% solution needed
given:
hydrogen peroxide in 8% solution:
{{{.8a}}} ml
hydrogen peroxide in 3% solution:
{{{.3b}}} ml
-----------------
{{{(.08a + .03b)/500 = .04}}}
{{{.08a + .03b = .04*500}}}
{{{.08a + .03b = 20}}}
(1) {{{8a + 3b = 2000}}}
and
(2) {{{a + b = 500}}}
Multiply both sides of (2) by {{{3}}}
and subtract (2) from (1)
(1) {{{8a + 3b = 2000}}}
(2) {{{-3a - 3b = -1500}}}
{{{5a = 500}}}
{{{a = 100}}}
and, since
{{{a + b = 500}}}
{{{100 + b = 500}}}
{{{b = 400}}}
100 ml of 8% solution and 400 ml of 3% solution are needed
check:
{{{.08a + .03b = 20}}}
{{{.08*100 + .03*400 = 20}}}
{{{8 + 12 = 20}}}
{{{20 = 20}}}
OK