Question 399532
In words:
(ml of active ingredient)/(ml of total solution) = 3%
Let {{{a}}} = ml of 9% solution to use
Let {{{b}}} = ml of 2% solution to use
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given:
{{{.09a}}} = ml of active ingredient in 9% solution
{{{.02b}}} = ml of active ingredient in 2% solution
(1) {{{a + b = 18}}} ml
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(2) {{{(.09a + .02b)/ 18 = .03}}}
(2) {{{.09a + .02b = .54}}}
(2) {{{9a + 2b = 54}}}
Multiply both sides of (1) by {{{2}}}
and subtract (1) from (2)
(2) {{{9a + 2b = 54}}}
(1) {{{-2a - 2b = -36}}}
{{{7a = 18}}}
{{{a = 18/7}}} ml
and, from (1)
(1) {{{a + b = 18}}}
{{{b = 18 - 18/7}}}
{{{b = (126 - 18)/7}}}
{{{b = 108/7}}} ml
18/7 ml of 9% solution must be used
108/7 ml of 2% solution must be used
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check answer:
(2) {{{(.09a + .02b)/ 18 = .03}}}
(2) {{{(.09*(18/7) + .02*(108/7))/ 18 = .03}}}
(2) {{{(9*(18/700) + 2*(108/700))/ 18 = 3/100}}}
(2) {{{(9*(18/700) + 2*(108/700))/ 18 = 21/700}}}
(2) {{{162 + 216 = 18*21}}}
(2) {{{378 = 378}}}
OK