Your chemistry professor gives you a 5 gallon jar containing 2 gallons of 40% alcohol. He asks you to reduce the concentration to 25%. How much water must you add to the jar?

Question

Your chemistry professor gives you a 5 gallon jar containing 2 gallons of 40% alcohol. He asks you to reduce the concentration to 25%. How much water must you add to the jar?

1 Answer

Impact of this question

1679 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-20T03:51:18

$3$ $3$ gallons

Explanation:

The context can be modelled by a general equation:

$% alcohol = \frac{gal alcohol}{gal solution}$ $% "alcohol"="gal alcohol"/"gal solution"$

Using the example, $40 % alcohol = \frac{2 gal alcohol}{5 gal} \cdot 100 %$ $40% "alcohol"=("2 gal alcohol")/("5 gal")*100%$ , we can set up another equation to solve for the number of galloons added.

Let $x$ $x$ be the number of gallons added.

$25 % alcohol = \frac{2 gal alcohol}{5 gal water + x gal water} \cdot 100 %$ $25% "alcohol"=("2 gal alcohol")/("5 gal water"+"x gal water")*100%$

$25 % alcohol \div 100 % = \frac{2 gal alcohol}{5 gal water + x gal water} \cdot 100 % \div 100 %$ $25% "alcohol"color(red)(-:100%)=("2 gal alcohol")/("5 gal water"+"x gal water")*100%color(red)(-:100%)$

$0.25$ $0.25$ $alcohol = \frac{2 gal alcohol}{5 gal water + x gal water}$ $"alcohol"=("2 gal alcohol")/("5 gal water"+"x gal water")$

$0.25$ $0.25$ $alcohol \cdot (5 gal water + x gal water) = 2 gal alcohol$ $"alcohol"*("5 gal water"+"x gal water")="2 gal alcohol"$

$0.25$ $0.25$ $alcohol \div 0.25$ $"alcohol"color(red)(-:0.25)$ $alcohol \cdot (5 gal water + x gal water) = 2 gal alcohol \div 0.25$ $color(red)("alcohol")*("5 gal water"+"x gal water")="2 gal alcohol"color(red)(-:0.25)$ $alcohol$ $color(red)("alcohol")$

$5 gal water+ x$ $"5 gal water+"x"$ $water$ $"water"$ $gal = 8$ $"gal"="8$ $gal$ $"gal"$

$x gal water$ $"x gal water"$ $=$ $=$ $3 gal water$ $"3 gal water"$

$:.$ , $3$ gallons of water must be added.

Science

Math

Humanities

... and beyond

Your chemistry professor gives you a 5 gallon jar containing 2 gallons of 40% alcohol. He asks you to reduce the concentration to 25%. How much water must you add to the jar?

1 Answer

Explanation:

Related questions

Impact of this question