Question 209326
What might help you is to always
remember that percent means
"per one-hundred", so whenever
you see %, you must divide by
100.
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A good question to ask with this
problem is: "How much water and
how much alcohol end up in the
final solution?
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Let {{{a}}}= liters of the 5% solution added
Let {{{b}}}= liters of the 25% solution added
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The equation to solve in words is:
(alcohol in 5% solution)+(alcohol in 25% soltion)/(alcohol + water in 20% solution) = 20%
So, I can write:
(1) {{{(.05a + .25b) / 8 = .2}}}
(2) {{{a + b = 8}}}
Multiply both sides of (1) by {{{8}}}
(1) {{{.05a + .25b  = 8*.2}}}
(1) {{{.05a + .25b = 1.6}}}
Multiply both sides of (2) by {{{.05}}} and subtract from (1)
(2) {{{.05a + .05b = .05*8}}}
(2) {{{.05a + .05b = .4}}}
And, subtracting:
(1) {{{.05a + .25b = 1.6}}}
(2) {{{-.05a - .05b = -.4}}}
{{{.2b = 1.2}}}
{{{b = 6}}}
She should use 6 liters of the 25% solution
check answer:
(2) {{{a + b = 8}}}
{{{a + 6 = 8}}}
{{{a = 2}}}
Go back to (1)
(1) {{{(.05a + .25b) / 8 = .2}}}
{{{(.05*2 + .25*6) / 8 = .2}}}
{{{.05*2 + .25*6 = 1.6}}}
{{{.1 + 1.5 = 1.6}}}
{{{1.6 = 1.6}}}
It always helps if you can sum up the problem in
an equation with words like I did (It helps me a lot)