Question 365004
Let {{{a}}} = liters of pure acid to be added
Let {{{b}}} = liters of 10% acid solution to be added
given:
(1) {{{a + b = 90}}}
(2) {{{(a + .1b)/90 = .75}}}
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From (2):
(2) {{{a +  .1b = 67.5}}}
(2) {{{10a + b = 675}}}
Subtract (1) from (2)
(2) {{{10a + b = 675}}}
(1) {{{-a - b = -90}}}
{{{9a = 585}}}
{{{a = 65}}}
And, since
 {{{a + b = 90}}}
{{{65 + b = 90}}}
{{{b = 25}}}
65 liters of pure acid and 25 liters of 10% solution are needed
check answer:
 {{{(a + .1b)/90 = .75}}}
{{{(65 + .1*25)/90 = .75}}}
{{{67.5/90 = .75}}}
{{{67.5 = .75*90}}}
{{{67.5 = 67.5}}}
OK