Question

Sharon has two solutions available in the lab, one solution with 6% alcohol and another with 11% alcohol. How much of each should she mix together to obtain 10 gallons of a solution that contains 7% alcohol?

Answer 1

8 gallons at 6%
2 gallons at 11%

Explanation:

Let the solution measure of 6% concentration be `S_6`
Let the solution measure of 11% concentration be `S_11`

For concentrations we have:

`[S_6xx6/100]+[S_11xx11/100]=10xxxx7/100`

`(6S_6)/100+(11S_11)/100=7/10" "......................Equation(1)`

For volume we have:

`S_6+S_11=10`

Thus `S_6=10-S_11" ".......................Equation(2)`
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Use `Eqn(2)` to substitute for `S_6` in `Eqn(1)`

`color(green)( (6color(red) (S_6))/100+(11S_11)/100=7/10 color(white)("d")->color(white)("dd")(6(color(red) (10-S_11)))/100+(11S_11)/100=7/10`

`color(white)("dddddddddddddddd")->color(white)("ddd")-(6S_11)/100color(white)("d")+(11S_11)/100 =7/10-6/10`

`color(white)("dddddddddddddddd")->color(white)("dddddddddddddd")(5S_11)/100=1/10`

`color(white)("dddddddddddddddd")->color(white)("dddddd")S_11=1/10xx100/5=2" gallons"`

From this `S_6=10-2=8" gallons"`